x(x+6)=90

Solution for x(x+6)=90 equation:

x(x+6)=90

We move all terms to the left:

x(x+6)-(90)=0

We multiply parentheses

x^2+6x-90=0

a = 1; b = 6; c = -90;
Δ = b2-4ac
Δ = 62-4·1·(-90)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{11}}{2*1}=\frac{-6-6\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{11}}{2*1}=\frac{-6+6\sqrt{11}}{2}
$