2x^2-50x=83

Solution for 2x^2-50x=83 equation:

2x^2-50x=83

We move all terms to the left:

2x^2-50x-(83)=0

a = 2; b = -50; c = -83;
Δ = b2-4ac
Δ = -502-4·2·(-83)
Δ = 3164
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:

$\sqrt{\Delta}=\sqrt{3164}=\sqrt{4*791}=\sqrt{4}*\sqrt{791}=2\sqrt{791}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{791}}{2*2}=\frac{50-2\sqrt{791}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{791}}{2*2}=\frac{50+2\sqrt{791}}{4}
$