$2x^2+5x-3 \,=\, 0$ is a given quadratic equation. It is given that we have to solve this quadratic equation by quadratic formula method in this maths problem.

For solving the quadratic equation $2x^2+5x-3 \,=\, 0$, compare this equation with the standard form quadratic equation $ax^2+bx+c \,=\, 0$. It helps us to know the literal coefficients of $x^2$ and $x$ and also the constant.

- $a \,=\, 2$
- $b \,=\, 5$
- $c \,=\, -3$

Now, use the quadratic formula to find the roots or zeros of the quadratic equation by substituting the values of $a$, $b$ and $c$.

$x$ $\,=\,$ $\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$

$\implies$ $x$ $\,=\,$ $\dfrac{-5 \pm \sqrt{5^2-4 \times 2 \times (-3)}}{2 \times 2}$

The substitution of $a$, $b$ and $c$ in quadratic formula gives us an equation and we have to solve it for solving the value of $x$ by simplification.

$\implies$ $x$ $\,=\,$ $\dfrac{-5 \pm \sqrt{25-8 \times (-3)}}{4}$

$\implies$ $x$ $\,=\,$ $\dfrac{-5 \pm \sqrt{25+24}}{4}$

$\implies$ $x$ $\,=\,$ $\dfrac{-5 \pm \sqrt{49}}{4}$

$\implies$ $x$ $\,=\,$ $\dfrac{-5 \pm 7}{4}$

Now, take plus sign in the first case and minus sign in the second case.

$\implies$ $x$ $\,=\,$ $\dfrac{-5+7}{4}$ and $x$ $\,=\,$ $\dfrac{-5-7}{4}$

$\implies$ $x$ $\,=\,$ $\dfrac{2}{4}$ and $x$ $\,=\,$ $\dfrac{-12}{4}$

$\implies$ $x$ $\,=\,$ $\dfrac{\cancel{2}}{\cancel{4}}$ and $x$ $\,=\,$ $\dfrac{-\cancel{12}}{\cancel{4}}$

$\implies$ $x$ $\,=\,$ $\dfrac{1}{2}$ and $x$ $\,=\,$ $-3$

The given quadratic expression $2x^2+5x-3$ is equal to zero when $x \,=\, -3$ and $x \,=\, \dfrac{1}{2}$. Therefore, the solution set for the given quadratic equation is $x \,=\, \Big\{-3, \dfrac{1}{2}\Big\}$

Latest Math Topics

Jan 06, 2023

Jan 03, 2023

Jan 01, 2023

Dec 26, 2022

Dec 08, 2022

Latest Math Problems

Nov 25, 2022

Nov 02, 2022

Oct 26, 2022

Oct 24, 2022

Sep 30, 2022

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved