8x=4x^2-600

Solution for 8x=4x^2-600 equation:

8x=4x^2-600

We move all terms to the left:

8x-(4x^2-600)=0

We get rid of parentheses

-4x^2+8x+600=0

a = -4; b = 8; c = +600;
Δ = b2-4ac
Δ = 82-4·(-4)·600
Δ = 9664
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:

$\sqrt{\Delta}=\sqrt{9664}=\sqrt{64*151}=\sqrt{64}*\sqrt{151}=8\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{151}}{2*-4}=\frac{-8-8\sqrt{151}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{151}}{2*-4}=\frac{-8+8\sqrt{151}}{-8}
$