r^2-10r=50

Solution for r^2-10r=50 equation:

r^2-10r=50

We move all terms to the left:

r^2-10r-(50)=0

a = 1; b = -10; c = -50;
Δ = b2-4ac
Δ = -102-4·1·(-50)
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{-(-10)-10\sqrt{3}}{2*1}=\frac{10-10\sqrt{3}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{3}}{2*1}=\frac{10+10\sqrt{3}}{2}
$