5r^2-36=10r

Solution for 5r^2-36=10r equation:

5r^2-36=10r

We move all terms to the left:

5r^2-36-(10r)=0

a = 5; b = -10; c = -36;
Δ = b2-4ac
Δ = -102-4·5·(-36)
Δ = 820
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:

$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{205}}{2*5}=\frac{10-2\sqrt{205}}{10}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{205}}{2*5}=\frac{10+2\sqrt{205}}{10}
$