x(x+10)=10

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

x(x+10)=10

We move all terms to the left:

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

We multiply parentheses

x^2+10x-10=0

a = 1; b = 10; c = -10;
Δ = b2-4ac
Δ = 102-4·1·(-10)
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{35}}{2*1}=\frac{-10-2\sqrt{35}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{35}}{2*1}=\frac{-10+2\sqrt{35}}{2}
$