x^2-21x+73.5=0

Solution for x^2-21x+73.5=0 equation:

x^2-21x+73.5=0

a = 1; b = -21; c = +73.5;
Δ = b2-4ac
Δ = -212-4·1·73.5
Δ = 147
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:

$\sqrt{\Delta}=\sqrt{147}=\sqrt{49*3}=\sqrt{49}*\sqrt{3}=7\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-7\sqrt{3}}{2*1}=\frac{21-7\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+7\sqrt{3}}{2*1}=\frac{21+7\sqrt{3}}{2}
$