150x-4x2-250=0

Solution for 150x-4x2-250=0 equation:

150x-4x^2-250=0

a = -4; b = 150; c = -250;
Δ = b2-4ac
Δ = 1502-4·(-4)·(-250)
Δ = 18500
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:

$\sqrt{\Delta}=\sqrt{18500}=\sqrt{100*185}=\sqrt{100}*\sqrt{185}=10\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-10\sqrt{185}}{2*-4}=\frac{-150-10\sqrt{185}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+10\sqrt{185}}{2*-4}=\frac{-150+10\sqrt{185}}{-8}
$