3x+2x(x-9)=8x+x+2

Solution for 3x+2x(x-9)=8x+x+2 equation:

3x+2x(x-9)=8x+x+2

We move all terms to the left:

3x+2x(x-9)-(8x+x+2)=0

We add all the numbers together, and all the variables

3x+2x(x-9)-(9x+2)=0

We multiply parentheses

2x^2+3x-18x-(9x+2)=0

We get rid of parentheses

2x^2+3x-18x-9x-2=0

We add all the numbers together, and all the variables

2x^2-24x-2=0

a = 2; b = -24; c = -2;
Δ = b2-4ac
Δ = -242-4·2·(-2)
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{37}}{2*2}=\frac{24-4\sqrt{37}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{37}}{2*2}=\frac{24+4\sqrt{37}}{4}
$