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

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

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

We move all terms to the left:

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

We multiply parentheses

3x^2+12x-((x+4)24)=0


We calculate terms in parentheses: -((x+4)24), so:

(x+4)24

We multiply parentheses

24x+96

Back to the equation:

-(24x+96)


We get rid of parentheses

3x^2+12x-24x-96=0

We add all the numbers together, and all the variables

3x^2-12x-96=0

a = 3; b = -12; c = -96;
Δ = b2-4ac
Δ = -122-4·3·(-96)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-36}{2*3}=\frac{-24}{6}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+36}{2*3}=\frac{48}{6}
=8
$