32+4x=3x^2

Solution for 32+4x=3x^2 equation:

32+4x=3x^2

We move all terms to the left:

32+4x-(3x^2)=0

determiningTheFunctionDomain
-3x^2+4x+32=0

a = -3; b = 4; c = +32;
Δ = b2-4ac
Δ = 42-4·(-3)·32
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-20}{2*-3}=\frac{-24}{-6}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+20}{2*-3}=\frac{16}{-6}
=-2+2/3
$