32x^2-x-33=0

Solution for 32x^2-x-33=0 equation:

32x^2-x-33=0

We add all the numbers together, and all the variables

32x^2-1x-33=0

a = 32; b = -1; c = -33;
Δ = b2-4ac
Δ = -12-4·32·(-33)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-65}{2*32}=\frac{-64}{64}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+65}{2*32}=\frac{66}{64}
=1+1/32
$