(3x+6)(x+8)=6x(x+5)

Solution for (3x+6)(x+8)=6x(x+5) equation:

(3x+6)(x+8)=6x(x+5)

We move all terms to the left:

(3x+6)(x+8)-(6x(x+5))=0

We multiply parentheses ..

(+3x^2+24x+6x+48)-(6x(x+5))=0


We calculate terms in parentheses: -(6x(x+5)), so:

6x(x+5)

We multiply parentheses

6x^2+30x

Back to the equation:

-(6x^2+30x)


We get rid of parentheses

3x^2-6x^2+24x+6x-30x+48=0

We add all the numbers together, and all the variables

-3x^2+48=0

a = -3; b = 0; c = +48;
Δ = b2-4ac
Δ = 02-4·(-3)·48
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*-3}=\frac{-24}{-6}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*-3}=\frac{24}{-6}
=-4
$