r^2-140r=-4800.18

Solution for r^2-140r=-4800.18 equation:

r^2-140r=-4800.18

We move all terms to the left:

r^2-140r-(-4800.18)=0

We add all the numbers together, and all the variables

r^2-140r+4800.18=0

a = 1; b = -140; c = +4800.18;
Δ = b2-4ac
Δ = -1402-4·1·4800.18
Δ = 399.28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-\sqrt{399.28}}{2*1}=\frac{140-\sqrt{399.28}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+\sqrt{399.28}}{2*1}=\frac{140+\sqrt{399.28}}{2}
$