2x^2-25x-50=5750

Solution for 2x^2-25x-50=5750 equation:

2x^2-25x-50=5750

We move all terms to the left:

2x^2-25x-50-(5750)=0

We add all the numbers together, and all the variables

2x^2-25x-5800=0

a = 2; b = -25; c = -5800;
Δ = b2-4ac
Δ = -252-4·2·(-5800)
Δ = 47025
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:

$\sqrt{\Delta}=\sqrt{47025}=\sqrt{225*209}=\sqrt{225}*\sqrt{209}=15\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-15\sqrt{209}}{2*2}=\frac{25-15\sqrt{209}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+15\sqrt{209}}{2*2}=\frac{25+15\sqrt{209}}{4}
$