6x(3+x)=24

Solution for 6x(3+x)=24 equation:

6x(3+x)=24

We move all terms to the left:

6x(3+x)-(24)=0

We add all the numbers together, and all the variables

6x(x+3)-24=0

We multiply parentheses

6x^2+18x-24=0

a = 6; b = 18; c = -24;
Δ = b2-4ac
Δ = 182-4·6·(-24)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-30}{2*6}=\frac{-48}{12}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+30}{2*6}=\frac{12}{12}
=1
$