x(x+50)=90

Solution for x(x+50)=90 equation:

x(x+50)=90

We move all terms to the left:

x(x+50)-(90)=0

We multiply parentheses

x^2+50x-90=0

a = 1; b = 50; c = -90;
Δ = b2-4ac
Δ = 502-4·1·(-90)
Δ = 2860
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:

$\sqrt{\Delta}=\sqrt{2860}=\sqrt{4*715}=\sqrt{4}*\sqrt{715}=2\sqrt{715}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{715}}{2*1}=\frac{-50-2\sqrt{715}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{715}}{2*1}=\frac{-50+2\sqrt{715}}{2}
$