2(x^2)-50x-213=0

Solution for 2(x^2)-50x-213=0 equation:

2(x^2)-50x-213=0

a = 2; b = -50; c = -213;
Δ = b2-4ac
Δ = -502-4·2·(-213)
Δ = 4204
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:

$\sqrt{\Delta}=\sqrt{4204}=\sqrt{4*1051}=\sqrt{4}*\sqrt{1051}=2\sqrt{1051}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{1051}}{2*2}=\frac{50-2\sqrt{1051}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{1051}}{2*2}=\frac{50+2\sqrt{1051}}{4}
$