100r^2-96r=12500

Solution for 100r^2-96r=12500 equation:

100r^2-96r=12500

We move all terms to the left:

100r^2-96r-(12500)=0

a = 100; b = -96; c = -12500;
Δ = b2-4ac
Δ = -962-4·100·(-12500)
Δ = 5009216
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:

$\sqrt{\Delta}=\sqrt{5009216}=\sqrt{64*78269}=\sqrt{64}*\sqrt{78269}=8\sqrt{78269}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-8\sqrt{78269}}{2*100}=\frac{96-8\sqrt{78269}}{200}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+8\sqrt{78269}}{2*100}=\frac{96+8\sqrt{78269}}{200}
$