2x^2-8x+6=1008

Solution for 2x^2-8x+6=1008 equation:

2x^2-8x+6=1008

We move all terms to the left:

2x^2-8x+6-(1008)=0

We add all the numbers together, and all the variables

2x^2-8x-1002=0

a = 2; b = -8; c = -1002;
Δ = b2-4ac
Δ = -82-4·2·(-1002)
Δ = 8080
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:

$\sqrt{\Delta}=\sqrt{8080}=\sqrt{16*505}=\sqrt{16}*\sqrt{505}=4\sqrt{505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{505}}{2*2}=\frac{8-4\sqrt{505}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{505}}{2*2}=\frac{8+4\sqrt{505}}{4}
$