2x^2-16=6x

Solution for 2x^2-16=6x equation:

2x^2-16=6x

We move all terms to the left:

2x^2-16-(6x)=0

a = 2; b = -6; c = -16;
Δ = b2-4ac
Δ = -62-4·2·(-16)
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{41}}{2*2}=\frac{6-2\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{41}}{2*2}=\frac{6+2\sqrt{41}}{4}
$