-48+6x+16x+2x^2=780

Solution for -48+6x+16x+2x^2=780 equation:

-48+6x+16x+2x^2=780

We move all terms to the left:

-48+6x+16x+2x^2-(780)=0

We add all the numbers together, and all the variables

2x^2+22x-828=0

a = 2; b = 22; c = -828;
Δ = b2-4ac
Δ = 222-4·2·(-828)
Δ = 7108
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:

$\sqrt{\Delta}=\sqrt{7108}=\sqrt{4*1777}=\sqrt{4}*\sqrt{1777}=2\sqrt{1777}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{1777}}{2*2}=\frac{-22-2\sqrt{1777}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{1777}}{2*2}=\frac{-22+2\sqrt{1777}}{4}
$