# How do you use the quadratic formula to solve for the roots in the following equation 4x^2+5x+2=2x^2+7x-1?

Jan 10, 2017

$x = \frac{1 + 2 i}{2}$ or $\frac{1 - 2 i}{2}$

#### Explanation:

$\to 4 {x}^{2} - 2 {x}^{2} + 5 x - 7 x + 2 - \left(- 1\right) = 0$
$\to 2 {x}^{2} - 2 x + 3 = 0$

And then you use the quadratic formula $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$ for the equation $a {x}^{2} + b x + c = 0$

and here we have got $a = 2$, $b = - 2$ and $c = 3$

hence $x = \frac{- \left(- 2\right) \pm \sqrt{{\left(- 2\right)}^{2} - 4 \times 2 \times 3}}{2 \times 2}$

= $\frac{2 \pm \sqrt{- 16}}{4} = \frac{2 \pm 4 i}{4}$

i.e. $x = \frac{1 + 2 i}{2}$ or $\frac{1 - 2 i}{2}$