x2-27x+90=0

Solution for x2-27x+90=0 equation:

x2-27x+90=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 = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{41}}{2*1}=\frac{27-3\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{41}}{2*1}=\frac{27+3\sqrt{41}}{2}
$