3x+2x(x-9)=8x+x-14

Solution for 3x+2x(x-9)=8x+x-14 equation:

3x+2x(x-9)=8x+x-14

We move all terms to the left:

3x+2x(x-9)-(8x+x-14)=0

We add all the numbers together, and all the variables

3x+2x(x-9)-(9x-14)=0

We multiply parentheses

2x^2+3x-18x-(9x-14)=0

We get rid of parentheses

2x^2+3x-18x-9x+14=0

We add all the numbers together, and all the variables

2x^2-24x+14=0

a = 2; b = -24; c = +14;
Δ = b2-4ac
Δ = -242-4·2·14
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{29}}{2*2}=\frac{24-4\sqrt{29}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{29}}{2*2}=\frac{24+4\sqrt{29}}{4}
$