2x-8x+x^2=375

Solution for 2x-8x+x^2=375 equation:

2x-8x+x^2=375

We move all terms to the left:

2x-8x+x^2-(375)=0

We add all the numbers together, and all the variables

x^2-6x-375=0

a = 1; b = -6; c = -375;
Δ = b2-4ac
Δ = -62-4·1·(-375)
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-16\sqrt{6}}{2*1}=\frac{6-16\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+16\sqrt{6}}{2*1}=\frac{6+16\sqrt{6}}{2}
$