4r2-94=8r

Solution for 4r2-94=8r equation:

4r^2-94=8r

We move all terms to the left:

4r^2-94-(8r)=0

a = 4; b = -8; c = -94;
Δ = b2-4ac
Δ = -82-4·4·(-94)
Δ = 1568
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:

$\sqrt{\Delta}=\sqrt{1568}=\sqrt{784*2}=\sqrt{784}*\sqrt{2}=28\sqrt{2}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-28\sqrt{2}}{2*4}=\frac{8-28\sqrt{2}}{8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+28\sqrt{2}}{2*4}=\frac{8+28\sqrt{2}}{8}
$