2*x^2-150x-25000=0

Solution for 2*x^2-150x-25000=0 equation:

2x^2-150x-25000=0

a = 2; b = -150; c = -25000;
Δ = b2-4ac
Δ = -1502-4·2·(-25000)
Δ = 222500
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:

$\sqrt{\Delta}=\sqrt{222500}=\sqrt{2500*89}=\sqrt{2500}*\sqrt{89}=50\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-50\sqrt{89}}{2*2}=\frac{150-50\sqrt{89}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+50\sqrt{89}}{2*2}=\frac{150+50\sqrt{89}}{4}
$