30x^2-45x-75=0

Solution for 30x^2-45x-75=0 equation:

30x^2-45x-75=0

a = 30; b = -45; c = -75;
Δ = b2-4ac
Δ = -452-4·30·(-75)
Δ = 11025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11025}=105$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-105}{2*30}=\frac{-60}{60}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+105}{2*30}=\frac{150}{60}
=2+1/2
$