7x^2-96x+256=0

Solution for 7x^2-96x+256=0 equation:

7x^2-96x+256=0

a = 7; b = -96; c = +256;
Δ = b2-4ac
Δ = -962-4·7·256
Δ = 2048
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:

$\sqrt{\Delta}=\sqrt{2048}=\sqrt{1024*2}=\sqrt{1024}*\sqrt{2}=32\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-32\sqrt{2}}{2*7}=\frac{96-32\sqrt{2}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+32\sqrt{2}}{2*7}=\frac{96+32\sqrt{2}}{14}
$