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

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

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

We move all terms to the left:

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

We multiply parentheses

2x^2+6x+3x+3-24=0

We add all the numbers together, and all the variables

2x^2+9x-21=0

a = 2; b = 9; c = -21;
Δ = b2-4ac
Δ = 92-4·2·(-21)
Δ = 249
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{-(9)-\sqrt{249}}{2*2}=\frac{-9-\sqrt{249}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{249}}{2*2}=\frac{-9+\sqrt{249}}{4}
$