(x+7)(3x)=(x+7)(24)

Solution for (x+7)(3x)=(x+7)(24) equation:

(x+7)(3x)=(x+7)(24)

We move all terms to the left:

(x+7)(3x)-((x+7)(24))=0

We multiply parentheses

3x^2+21x-((x+7)24)=0


We calculate terms in parentheses: -((x+7)24), so:

(x+7)24

We multiply parentheses

24x+168

Back to the equation:

-(24x+168)


We get rid of parentheses

3x^2+21x-24x-168=0

We add all the numbers together, and all the variables

3x^2-3x-168=0

a = 3; b = -3; c = -168;
Δ = b2-4ac
Δ = -32-4·3·(-168)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-45}{2*3}=\frac{-42}{6}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+45}{2*3}=\frac{48}{6}
=8
$