4x^2-64x+256=750

Solution for 4x^2-64x+256=750 equation:

4x^2-64x+256=750

We move all terms to the left:

4x^2-64x+256-(750)=0

We add all the numbers together, and all the variables

4x^2-64x-494=0

a = 4; b = -64; c = -494;
Δ = b2-4ac
Δ = -642-4·4·(-494)
Δ = 12000
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:

$\sqrt{\Delta}=\sqrt{12000}=\sqrt{400*30}=\sqrt{400}*\sqrt{30}=20\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-20\sqrt{30}}{2*4}=\frac{64-20\sqrt{30}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+20\sqrt{30}}{2*4}=\frac{64+20\sqrt{30}}{8}
$