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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(3x(x+24)), so:

3x(x+24)

We multiply parentheses

3x^2+72x

Back to the equation:

-(3x^2+72x)


We get rid of parentheses

-3x^2+3x-72x+24=0

We add all the numbers together, and all the variables

-3x^2-69x+24=0

a = -3; b = -69; c = +24;
Δ = b2-4ac
Δ = -692-4·(-3)·24
Δ = 5049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5049}=\sqrt{9*561}=\sqrt{9}*\sqrt{561}=3\sqrt{561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-3\sqrt{561}}{2*-3}=\frac{69-3\sqrt{561}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+3\sqrt{561}}{2*-3}=\frac{69+3\sqrt{561}}{-6}
$