x(x+40)=90

Solution for x(x+40)=90 equation:

x(x+40)=90

We move all terms to the left:

x(x+40)-(90)=0

We multiply parentheses

x^2+40x-90=0

a = 1; b = 40; c = -90;
Δ = b2-4ac
Δ = 402-4·1·(-90)
Δ = 1960
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:

$\sqrt{\Delta}=\sqrt{1960}=\sqrt{196*10}=\sqrt{196}*\sqrt{10}=14\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-14\sqrt{10}}{2*1}=\frac{-40-14\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+14\sqrt{10}}{2*1}=\frac{-40+14\sqrt{10}}{2}
$