416=2x^2-6x

Solution for 416=2x^2-6x equation:

416=2x^2-6x

We move all terms to the left:

416-(2x^2-6x)=0

We get rid of parentheses

-2x^2+6x+416=0

a = -2; b = 6; c = +416;
Δ = b2-4ac
Δ = 62-4·(-2)·416
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-58}{2*-2}=\frac{-64}{-4}
=+16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+58}{2*-2}=\frac{52}{-4}
=-13
$