x2-45x+500=0

Solution for x2-45x+500=0 equation:

x2-45x+500=0

We add all the numbers together, and all the variables

x^2-45x+500=0

a = 1; b = -45; c = +500;
Δ = b2-4ac
Δ = -452-4·1·500
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-5}{2*1}=\frac{40}{2}
=20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+5}{2*1}=\frac{50}{2}
=25
$