2x(10-x)=4

Solution for 2x(10-x)=4 equation:

2x(10-x)=4

We move all terms to the left:

2x(10-x)-(4)=0

We add all the numbers together, and all the variables

2x(-1x+10)-4=0

We multiply parentheses

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

a = -2; b = 20; c = -4;
Δ = b2-4ac
Δ = 202-4·(-2)·(-4)
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{23}}{2*-2}=\frac{-20-4\sqrt{23}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{23}}{2*-2}=\frac{-20+4\sqrt{23}}{-4}
$