2x^2-6x=416

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

2x^2-6x=416

We move all terms to the left:

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