3x+x(4x+1)=24

Solution for 3x+x(4x+1)=24 equation:

3x+x(4x+1)=24

We move all terms to the left:

3x+x(4x+1)-(24)=0

We multiply parentheses

4x^2+3x+x-24=0

We add all the numbers together, and all the variables

4x^2+4x-24=0

a = 4; b = 4; c = -24;
Δ = b2-4ac
Δ = 42-4·4·(-24)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-20}{2*4}=\frac{-24}{8}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+20}{2*4}=\frac{16}{8}
=2
$