x2-27x+180=0

Solution for x2-27x+180=0 equation:

x2-27x+180=0

We add all the numbers together, and all the variables

x^2-27x+180=0

a = 1; b = -27; c = +180;
Δ = b2-4ac
Δ = -272-4·1·180
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3}{2*1}=\frac{24}{2}
=12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3}{2*1}=\frac{30}{2}
=15
$