x^2-30x-218.75=0

Solution for x^2-30x-218.75=0 equation:

x^2-30x-218.75=0

a = 1; b = -30; c = -218.75;
Δ = b2-4ac
Δ = -302-4·1·(-218.75)
Δ = 1775
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:

$\sqrt{\Delta}=\sqrt{1775}=\sqrt{25*71}=\sqrt{25}*\sqrt{71}=5\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-5\sqrt{71}}{2*1}=\frac{30-5\sqrt{71}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+5\sqrt{71}}{2*1}=\frac{30+5\sqrt{71}}{2}
$