3(2x+3)4x+2=21

Solution for 3(2x+3)4x+2=21 equation:

3(2x+3)4x+2=21

We move all terms to the left:

3(2x+3)4x+2-(21)=0

We add all the numbers together, and all the variables

3(2x+3)4x-19=0

We multiply parentheses

24x^2+36x-19=0

a = 24; b = 36; c = -19;
Δ = b2-4ac
Δ = 362-4·24·(-19)
Δ = 3120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3120}=\sqrt{16*195}=\sqrt{16}*\sqrt{195}=4\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{195}}{2*24}=\frac{-36-4\sqrt{195}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{195}}{2*24}=\frac{-36+4\sqrt{195}}{48}
$