6x(x+2)=2(x+4)

Solution for 6x(x+2)=2(x+4) equation:

6x(x+2)=2(x+4)

We move all terms to the left:

6x(x+2)-(2(x+4))=0

We multiply parentheses

6x^2+12x-(2(x+4))=0


We calculate terms in parentheses: -(2(x+4)), so:

2(x+4)

We multiply parentheses

2x+8

Back to the equation:

-(2x+8)


We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2+10x-8=0

a = 6; b = 10; c = -8;
Δ = b2-4ac
Δ = 102-4·6·(-8)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{73}}{2*6}=\frac{-10-2\sqrt{73}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{73}}{2*6}=\frac{-10+2\sqrt{73}}{12}
$