(x+9)(x+8)+2x=2(x+8)+4(x+9)

Solution for (x+9)(x+8)+2x=2(x+8)+4(x+9) equation:

(x+9)(x+8)+2x=2(x+8)+4(x+9)

We move all terms to the left:

(x+9)(x+8)+2x-(2(x+8)+4(x+9))=0

We add all the numbers together, and all the variables

2x+(x+9)(x+8)-(2(x+8)+4(x+9))=0

We multiply parentheses ..

(+x^2+8x+9x+72)+2x-(2(x+8)+4(x+9))=0


We calculate terms in parentheses: -(2(x+8)+4(x+9)), so:

2(x+8)+4(x+9)

We multiply parentheses

2x+4x+16+36

We add all the numbers together, and all the variables

6x+52

Back to the equation:

-(6x+52)


We get rid of parentheses

x^2+8x+9x+2x-6x+72-52=0

We add all the numbers together, and all the variables

x^2+13x+20=0

a = 1; b = 13; c = +20;
Δ = b2-4ac
Δ = 132-4·1·20
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{89}}{2*1}=\frac{-13-\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{89}}{2*1}=\frac{-13+\sqrt{89}}{2}
$