3x(2x+1)+24=42

Solution for 3x(2x+1)+24=42 equation:

3x(2x+1)+24=42

We move all terms to the left:

3x(2x+1)+24-(42)=0

We add all the numbers together, and all the variables

3x(2x+1)-18=0

We multiply parentheses

6x^2+3x-18=0

a = 6; b = 3; c = -18;
Δ = b2-4ac
Δ = 32-4·6·(-18)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-21}{2*6}=\frac{-24}{12}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+21}{2*6}=\frac{18}{12}
=1+1/2
$