2x^2-12x=784

Solution for 2x^2-12x=784 equation:

2x^2-12x=784

We move all terms to the left:

2x^2-12x-(784)=0

a = 2; b = -12; c = -784;
Δ = b2-4ac
Δ = -122-4·2·(-784)
Δ = 6416
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:

$\sqrt{\Delta}=\sqrt{6416}=\sqrt{16*401}=\sqrt{16}*\sqrt{401}=4\sqrt{401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{401}}{2*2}=\frac{12-4\sqrt{401}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{401}}{2*2}=\frac{12+4\sqrt{401}}{4}
$