(2x+8)+(3x-14)(3x-14)=180

Solution for (2x+8)+(3x-14)(3x-14)=180 equation:

(2x+8)+(3x-14)(3x-14)=180

We move all terms to the left:

(2x+8)+(3x-14)(3x-14)-(180)=0

We get rid of parentheses

2x+(3x-14)(3x-14)+8-180=0

We multiply parentheses ..

(+9x^2-42x-42x+196)+2x+8-180=0

We add all the numbers together, and all the variables

(+9x^2-42x-42x+196)+2x-172=0

We get rid of parentheses

9x^2-42x-42x+2x+196-172=0

We add all the numbers together, and all the variables

9x^2-82x+24=0

a = 9; b = -82; c = +24;
Δ = b2-4ac
Δ = -822-4·9·24
Δ = 5860
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:

$\sqrt{\Delta}=\sqrt{5860}=\sqrt{4*1465}=\sqrt{4}*\sqrt{1465}=2\sqrt{1465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{1465}}{2*9}=\frac{82-2\sqrt{1465}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{1465}}{2*9}=\frac{82+2\sqrt{1465}}{18}
$