2(2x2+45x)=424

Solution for 2(2x2+45x)=424 equation:

2(2x^2+45x)=424

We move all terms to the left:

2(2x^2+45x)-(424)=0

We multiply parentheses

4x^2+90x-424=0

a = 4; b = 90; c = -424;
Δ = b2-4ac
Δ = 902-4·4·(-424)
Δ = 14884
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14884}=122$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-122}{2*4}=\frac{-212}{8}
=-26+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+122}{2*4}=\frac{32}{8}
=4
$