10x(x-10)=100

Solution for 10x(x-10)=100 equation:

10x(x-10)=100

We move all terms to the left:

10x(x-10)-(100)=0

We multiply parentheses

10x^2-100x-100=0

a = 10; b = -100; c = -100;
Δ = b2-4ac
Δ = -1002-4·10·(-100)
Δ = 14000
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:

$\sqrt{\Delta}=\sqrt{14000}=\sqrt{400*35}=\sqrt{400}*\sqrt{35}=20\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{35}}{2*10}=\frac{100-20\sqrt{35}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{35}}{2*10}=\frac{100+20\sqrt{35}}{20}
$