50x2-75x-24=0

Solution for 50x2-75x-24=0 equation:

50x^2-75x-24=0

a = 50; b = -75; c = -24;
Δ = b2-4ac
Δ = -752-4·50·(-24)
Δ = 10425
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:

$\sqrt{\Delta}=\sqrt{10425}=\sqrt{25*417}=\sqrt{25}*\sqrt{417}=5\sqrt{417}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{417}}{2*50}=\frac{75-5\sqrt{417}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{417}}{2*50}=\frac{75+5\sqrt{417}}{100}
$