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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -((x+2)24), so:

(x+2)24

We multiply parentheses

24x+48

Back to the equation:

-(24x+48)


We get rid of parentheses

3x^2+6x-24x-48=0

We add all the numbers together, and all the variables

3x^2-18x-48=0

a = 3; b = -18; c = -48;
Δ = b2-4ac
Δ = -182-4·3·(-48)
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*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+30}{2*3}=\frac{48}{6}
=8
$