(x^2)/4+8=64

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

(x^2)/4+8=64

We move all terms to the left:

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

We add all the numbers together, and all the variables

x^2/4-56=0

We multiply all the terms by the denominator


x^2-56*4=0

We add all the numbers together, and all the variables

x^2-224=0

a = 1; b = 0; c = -224;
Δ = b2-4ac
Δ = 02-4·1·(-224)
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{14}}{2*1}=\frac{0-8\sqrt{14}}{2}
=-\frac{8\sqrt{14}}{2}
=-4\sqrt{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{14}}{2*1}=\frac{0+8\sqrt{14}}{2}
=\frac{8\sqrt{14}}{2}
=4\sqrt{14}
$