32-12x-9x^2=0

Solution for 32-12x-9x^2=0 equation:

32-12x-9x^2=0

a = -9; b = -12; c = +32;
Δ = b2-4ac
Δ = -122-4·(-9)·32
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-36}{2*-9}=\frac{-24}{-18}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+36}{2*-9}=\frac{48}{-18}
=-2+2/3
$