(x-5)(x+10)=10

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

(x-5)(x+10)=10

We move all terms to the left:

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

We multiply parentheses ..

(+x^2+10x-5x-50)-10=0

We get rid of parentheses

x^2+10x-5x-50-10=0

We add all the numbers together, and all the variables

x^2+5x-60=0

a = 1; b = 5; c = -60;
Δ = b2-4ac
Δ = 52-4·1·(-60)
Δ = 265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{265}}{2*1}=\frac{-5-\sqrt{265}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{265}}{2*1}=\frac{-5+\sqrt{265}}{2}
$