r^2-15r-18.75=0

Solution for r^2-15r-18.75=0 equation:

r^2-15r-18.75=0

a = 1; b = -15; c = -18.75;
Δ = b2-4ac
Δ = -152-4·1·(-18.75)
Δ = 300
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-10\sqrt{3}}{2*1}=\frac{15-10\sqrt{3}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+10\sqrt{3}}{2*1}=\frac{15+10\sqrt{3}}{2}
$