8x(x+2)-8=2x(2+x)+9

Solution for 8x(x+2)-8=2x(2+x)+9 equation:

8x(x+2)-8=2x(2+x)+9

We move all terms to the left:

8x(x+2)-8-(2x(2+x)+9)=0

We add all the numbers together, and all the variables

8x(x+2)-(2x(x+2)+9)-8=0

We multiply parentheses

8x^2+16x-(2x(x+2)+9)-8=0


We calculate terms in parentheses: -(2x(x+2)+9), so:

2x(x+2)+9

We multiply parentheses

2x^2+4x+9

Back to the equation:

-(2x^2+4x+9)


We get rid of parentheses

8x^2-2x^2+16x-4x-9-8=0

We add all the numbers together, and all the variables

6x^2+12x-17=0

a = 6; b = 12; c = -17;
Δ = b2-4ac
Δ = 122-4·6·(-17)
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{138}}{2*6}=\frac{-12-2\sqrt{138}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{138}}{2*6}=\frac{-12+2\sqrt{138}}{12}
$