2x(10-2x)=12

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

2x(10-2x)=12

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-4x^2+20x-12=0

a = -4; b = 20; c = -12;
Δ = b2-4ac
Δ = 202-4·(-4)·(-12)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{13}}{2*-4}=\frac{-20-4\sqrt{13}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{13}}{2*-4}=\frac{-20+4\sqrt{13}}{-8}
$