32x^2-108x-45=0

Solution for 32x^2-108x-45=0 equation:

32x^2-108x-45=0

a = 32; b = -108; c = -45;
Δ = b2-4ac
Δ = -1082-4·32·(-45)
Δ = 17424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17424}=132$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-132}{2*32}=\frac{-24}{64}
=-3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+132}{2*32}=\frac{240}{64}
=3+3/4
$