(x+10)(2x-20)=10

Solution for (x+10)(2x-20)=10 equation:

(x+10)(2x-20)=10

We move all terms to the left:

(x+10)(2x-20)-(10)=0

We multiply parentheses ..

(+2x^2-20x+20x-200)-10=0

We get rid of parentheses

2x^2-20x+20x-200-10=0

We add all the numbers together, and all the variables

2x^2-210=0

a = 2; b = 0; c = -210;
Δ = b2-4ac
Δ = 02-4·2·(-210)
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{105}}{2*2}=\frac{0-4\sqrt{105}}{4}
=-\frac{4\sqrt{105}}{4}
=-\sqrt{105}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{105}}{2*2}=\frac{0+4\sqrt{105}}{4}
=\frac{4\sqrt{105}}{4}
=\sqrt{105}
$