4r^2-96r=196

Solution for 4r^2-96r=196 equation:

4r^2-96r=196

We move all terms to the left:

4r^2-96r-(196)=0

a = 4; b = -96; c = -196;
Δ = b2-4ac
Δ = -962-4·4·(-196)
Δ = 12352
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:

$\sqrt{\Delta}=\sqrt{12352}=\sqrt{64*193}=\sqrt{64}*\sqrt{193}=8\sqrt{193}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-8\sqrt{193}}{2*4}=\frac{96-8\sqrt{193}}{8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+8\sqrt{193}}{2*4}=\frac{96+8\sqrt{193}}{8}
$