5r^2-55r-90=0

Solution for 5r^2-55r-90=0 equation:

5r^2-55r-90=0

a = 5; b = -55; c = -90;
Δ = b2-4ac
Δ = -552-4·5·(-90)
Δ = 4825
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:

$\sqrt{\Delta}=\sqrt{4825}=\sqrt{25*193}=\sqrt{25}*\sqrt{193}=5\sqrt{193}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-5\sqrt{193}}{2*5}=\frac{55-5\sqrt{193}}{10}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+5\sqrt{193}}{2*5}=\frac{55+5\sqrt{193}}{10}
$