(6x-9)+(4x+2)x=180

Solution for (6x-9)+(4x+2)x=180 equation:

(6x-9)+(4x+2)x=180

We move all terms to the left:

(6x-9)+(4x+2)x-(180)=0

We multiply parentheses

4x^2+(6x-9)+2x-180=0

We get rid of parentheses

4x^2+6x+2x-9-180=0

We add all the numbers together, and all the variables

4x^2+8x-189=0

a = 4; b = 8; c = -189;
Δ = b2-4ac
Δ = 82-4·4·(-189)
Δ = 3088
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:

$\sqrt{\Delta}=\sqrt{3088}=\sqrt{16*193}=\sqrt{16}*\sqrt{193}=4\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{193}}{2*4}=\frac{-8-4\sqrt{193}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{193}}{2*4}=\frac{-8+4\sqrt{193}}{8}
$