(x+2)(3x-7)=180

Solution for (x+2)(3x-7)=180 equation:

(x+2)(3x-7)=180

We move all terms to the left:

(x+2)(3x-7)-(180)=0

We multiply parentheses ..

(+3x^2-7x+6x-14)-180=0

We get rid of parentheses

3x^2-7x+6x-14-180=0

We add all the numbers together, and all the variables

3x^2-1x-194=0

a = 3; b = -1; c = -194;
Δ = b2-4ac
Δ = -12-4·3·(-194)
Δ = 2329
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{-(-1)-\sqrt{2329}}{2*3}=\frac{1-\sqrt{2329}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{2329}}{2*3}=\frac{1+\sqrt{2329}}{6}
$