4x^2+8x=64=0

Solution for 4x^2+8x=64=0 equation:

4x^2+8x=64=0

We move all terms to the left:

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

a = 4; b = 8; c = -64;
Δ = b2-4ac
Δ = 82-4·4·(-64)
Δ = 1088
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:

$\sqrt{\Delta}=\sqrt{1088}=\sqrt{64*17}=\sqrt{64}*\sqrt{17}=8\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{17}}{2*4}=\frac{-8-8\sqrt{17}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{17}}{2*4}=\frac{-8+8\sqrt{17}}{8}
$