(2x)(x+31)=124

Solution for (2x)(x+31)=124 equation:

(2x)(x+31)=124

We move all terms to the left:

(2x)(x+31)-(124)=0

We multiply parentheses

2x^2+62x-124=0

a = 2; b = 62; c = -124;
Δ = b2-4ac
Δ = 622-4·2·(-124)
Δ = 4836
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4836}=\sqrt{4*1209}=\sqrt{4}*\sqrt{1209}=2\sqrt{1209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-2\sqrt{1209}}{2*2}=\frac{-62-2\sqrt{1209}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+2\sqrt{1209}}{2*2}=\frac{-62+2\sqrt{1209}}{4}
$