4x(3x+1)=33

Solution for 4x(3x+1)=33 equation:

4x(3x+1)=33

We move all terms to the left:

4x(3x+1)-(33)=0

We multiply parentheses

12x^2+4x-33=0

a = 12; b = 4; c = -33;
Δ = b2-4ac
Δ = 42-4·12·(-33)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-40}{2*12}=\frac{-44}{24}
=-1+5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+40}{2*12}=\frac{36}{24}
=1+1/2
$