32x+3x=6+3x^2

Solution for 32x+3x=6+3x^2 equation:

32x+3x=6+3x^2

We move all terms to the left:

32x+3x-(6+3x^2)=0

We add all the numbers together, and all the variables

-(6+3x^2)+35x=0

We get rid of parentheses

-3x^2+35x-6=0

a = -3; b = 35; c = -6;
Δ = b2-4ac
Δ = 352-4·(-3)·(-6)
Δ = 1153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-\sqrt{1153}}{2*-3}=\frac{-35-\sqrt{1153}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{1153}}{2*-3}=\frac{-35+\sqrt{1153}}{-6}
$