X^2-27x=180/2

Solution for X^2-27x=180/2 equation:

X^2-27X=180/2

We move all terms to the left:

X^2-27X-(180/2)=0

We add all the numbers together, and all the variables

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