4r^2-94=8

Solution for 4r^2-94=8 equation:

4r^2-94=8

We move all terms to the left:

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

We add all the numbers together, and all the variables

4r^2-102=0

a = 4; b = 0; c = -102;
Δ = b2-4ac
Δ = 02-4·4·(-102)
Δ = 1632
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:

$\sqrt{\Delta}=\sqrt{1632}=\sqrt{16*102}=\sqrt{16}*\sqrt{102}=4\sqrt{102}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{102}}{2*4}=\frac{0-4\sqrt{102}}{8}
=-\frac{4\sqrt{102}}{8}
=-\frac{\sqrt{102}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{102}}{2*4}=\frac{0+4\sqrt{102}}{8}
=\frac{4\sqrt{102}}{8}
=\frac{\sqrt{102}}{2}
$