5r^2-10r-60=6

Solution for 5r^2-10r-60=6 equation:

5r^2-10r-60=6

We move all terms to the left:

5r^2-10r-60-(6)=0

We add all the numbers together, and all the variables

5r^2-10r-66=0

a = 5; b = -10; c = -66;
Δ = b2-4ac
Δ = -102-4·5·(-66)
Δ = 1420
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:

$\sqrt{\Delta}=\sqrt{1420}=\sqrt{4*355}=\sqrt{4}*\sqrt{355}=2\sqrt{355}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{355}}{2*5}=\frac{10-2\sqrt{355}}{10}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{355}}{2*5}=\frac{10+2\sqrt{355}}{10}
$