2x(x-10)=12

Solution for 2x(x-10)=12 equation:

2x(x-10)=12

We move all terms to the left:

2x(x-10)-(12)=0

We multiply parentheses

2x^2-20x-12=0

a = 2; b = -20; c = -12;
Δ = b2-4ac
Δ = -202-4·2·(-12)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{31}}{2*2}=\frac{20-4\sqrt{31}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{31}}{2*2}=\frac{20+4\sqrt{31}}{4}
$