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

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

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

We move all terms to the left:

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

We multiply parentheses

8x-(x(3x+8))+48=0


We calculate terms in parentheses: -(x(3x+8)), so:

x(3x+8)

We multiply parentheses

3x^2+8x

Back to the equation:

-(3x^2+8x)


We get rid of parentheses

-3x^2+8x-8x+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
$