3x(2x+1)=32

Solution for 3x(2x+1)=32 equation:

3x(2x+1)=32

We move all terms to the left:

3x(2x+1)-(32)=0

We multiply parentheses

6x^2+3x-32=0

a = 6; b = 3; c = -32;
Δ = b2-4ac
Δ = 32-4·6·(-32)
Δ = 777
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{-(3)-\sqrt{777}}{2*6}=\frac{-3-\sqrt{777}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{777}}{2*6}=\frac{-3+\sqrt{777}}{12}
$