x^2-18.5x+52.5=0

Solution for x^2-18.5x+52.5=0 equation:

x^2-18.5x+52.5=0

a = 1; b = -18.5; c = +52.5;
Δ = b2-4ac
Δ = -18.52-4·1·52.5
Δ = 132.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18.5)-\sqrt{132.25}}{2*1}=\frac{18.5-\sqrt{132.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18.5)+\sqrt{132.25}}{2*1}=\frac{18.5+\sqrt{132.25}}{2}
$