27x+x^2=90

Solution for 27x+x^2=90 equation:

27x+x^2=90

We move all terms to the left:

27x+x^2-(90)=0

a = 1; b = 27; c = -90;
Δ = b2-4ac
Δ = 272-4·1·(-90)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-33}{2*1}=\frac{-60}{2}
=-30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+33}{2*1}=\frac{6}{2}
=3
$