8x^2+4x=64

Solution for 8x^2+4x=64 equation:

8x^2+4x=64

We move all terms to the left:

8x^2+4x-(64)=0

a = 8; b = 4; c = -64;
Δ = b2-4ac
Δ = 42-4·8·(-64)
Δ = 2064
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:

$\sqrt{\Delta}=\sqrt{2064}=\sqrt{16*129}=\sqrt{16}*\sqrt{129}=4\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{129}}{2*8}=\frac{-4-4\sqrt{129}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{129}}{2*8}=\frac{-4+4\sqrt{129}}{16}
$