6x(x+2)=8(x+1)

Solution for 6x(x+2)=8(x+1) equation:

6x(x+2)=8(x+1)

We move all terms to the left:

6x(x+2)-(8(x+1))=0

We multiply parentheses

6x^2+12x-(8(x+1))=0


We calculate terms in parentheses: -(8(x+1)), so:

8(x+1)

We multiply parentheses

8x+8

Back to the equation:

-(8x+8)


We get rid of parentheses

6x^2+12x-8x-8=0

We add all the numbers together, and all the variables

6x^2+4x-8=0

a = 6; b = 4; c = -8;
Δ = b2-4ac
Δ = 42-4·6·(-8)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{13}}{2*6}=\frac{-4-4\sqrt{13}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{13}}{2*6}=\frac{-4+4\sqrt{13}}{12}
$