2(x-5)x=10

Solution for 2(x-5)x=10 equation:

2(x-5)x=10

We move all terms to the left:

2(x-5)x-(10)=0

We multiply parentheses

2x^2-10x-10=0

a = 2; b = -10; c = -10;
Δ = b2-4ac
Δ = -102-4·2·(-10)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{5}}{2*2}=\frac{10-6\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{5}}{2*2}=\frac{10+6\sqrt{5}}{4}
$