# How do you solve 2x^2-5x=-7 using the quadratic formula?

Feb 16, 2016

Solution is $\frac{5}{4} \pm i \frac{\sqrt{31}}{4}$

#### Explanation:

Quadratic formula $\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$ gives us the solution of equation $a {x}^{2} + b x + c = 0$. As the given equation is 2x^2−5x=−7 or 2x^2−5x+7=0 i.e. $a = 2$, $b = - 5$ and $c = 7$, hence solution is given by

$\frac{- \left(- 5\right) \pm \sqrt{{\left(- 5\right)}^{2} - 4 \cdot 2 \cdot 7}}{2 \cdot 2}$ i.e.

$\frac{5 \pm \sqrt{25 - 56}}{4}$

$\frac{5}{4} \pm i \frac{\sqrt{31}}{4}$