X2-20x+45=0

Solution for X2-20x+45=0 equation:

X2-20X+45=0

We add all the numbers together, and all the variables

X^2-20X+45=0

a = 1; b = -20; c = +45;
Δ = b2-4ac
Δ = -202-4·1·45
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{55}}{2*1}=\frac{20-2\sqrt{55}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{55}}{2*1}=\frac{20+2\sqrt{55}}{2}
$