100x^2+75x-144=0

Solution for 100x^2+75x-144=0 equation:

100x^2+75x-144=0

a = 100; b = 75; c = -144;
Δ = b2-4ac
Δ = 752-4·100·(-144)
Δ = 63225
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:

$\sqrt{\Delta}=\sqrt{63225}=\sqrt{225*281}=\sqrt{225}*\sqrt{281}=15\sqrt{281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-15\sqrt{281}}{2*100}=\frac{-75-15\sqrt{281}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+15\sqrt{281}}{2*100}=\frac{-75+15\sqrt{281}}{200}
$