4x+108=8x^2

Solution for 4x+108=8x^2 equation:

4x+108=8x^2

We move all terms to the left:

4x+108-(8x^2)=0

determiningTheFunctionDomain
-8x^2+4x+108=0

a = -8; b = 4; c = +108;
Δ = b2-4ac
Δ = 42-4·(-8)·108
Δ = 3472
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3472}=\sqrt{16*217}=\sqrt{16}*\sqrt{217}=4\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{217}}{2*-8}=\frac{-4-4\sqrt{217}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{217}}{2*-8}=\frac{-4+4\sqrt{217}}{-16}
$