x2-21x+90=0

Solution for x2-21x+90=0 equation:

x2-21x+90=0

We add all the numbers together, and all the variables

x^2-21x+90=0

a = 1; b = -21; c = +90;
Δ = b2-4ac
Δ = -212-4·1·90
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-9}{2*1}=\frac{12}{2}
=6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+9}{2*1}=\frac{30}{2}
=15
$