100b^2+75b-9=0

Solution for 100b^2+75b-9=0 equation:

100b^2+75b-9=0

a = 100; b = 75; c = -9;
Δ = b2-4ac
Δ = 752-4·100·(-9)
Δ = 9225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9225}=\sqrt{225*41}=\sqrt{225}*\sqrt{41}=15\sqrt{41}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-15\sqrt{41}}{2*100}=\frac{-75-15\sqrt{41}}{200}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+15\sqrt{41}}{2*100}=\frac{-75+15\sqrt{41}}{200}
$