(x-3)(3x+1)=32

Solution for (x-3)(3x+1)=32 equation:

(x-3)(3x+1)=32

We move all terms to the left:

(x-3)(3x+1)-(32)=0

We multiply parentheses ..

(+3x^2+x-9x-3)-32=0

We get rid of parentheses

3x^2+x-9x-3-32=0

We add all the numbers together, and all the variables

3x^2-8x-35=0

a = 3; b = -8; c = -35;
Δ = b2-4ac
Δ = -82-4·3·(-35)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-22}{2*3}=\frac{-14}{6}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+22}{2*3}=\frac{30}{6}
=5
$