2x(x-13)=120

Solution for 2x(x-13)=120 equation:

2x(x-13)=120

We move all terms to the left:

2x(x-13)-(120)=0

We multiply parentheses

2x^2-26x-120=0

a = 2; b = -26; c = -120;
Δ = b2-4ac
Δ = -262-4·2·(-120)
Δ = 1636
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:

$\sqrt{\Delta}=\sqrt{1636}=\sqrt{4*409}=\sqrt{4}*\sqrt{409}=2\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{409}}{2*2}=\frac{26-2\sqrt{409}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{409}}{2*2}=\frac{26+2\sqrt{409}}{4}
$