(X^2)/(x+180)=90

Solution for (X^2)/(x+180)=90 equation:

(X^2)/(X+180)=90

We move all terms to the left:

(X^2)/(X+180)-(90)=0


Domain of the equation: (X+180)!=0

We move all terms containing X to the left, all other terms to the right

X!=-180

X∈R


We multiply all the terms by the denominator


X^2-90*(X+180)=0

We multiply parentheses

X^2-90X-16200=0

a = 1; b = -90; c = -16200;
Δ = b2-4ac
Δ = -902-4·1·(-16200)
Δ = 72900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{72900}=270$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-270}{2*1}=\frac{-180}{2}
=-90
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+270}{2*1}=\frac{360}{2}
=180
$