(3x+7)(x-17)=180

Solution for (3x+7)(x-17)=180 equation:

(3x+7)(x-17)=180

We move all terms to the left:

(3x+7)(x-17)-(180)=0

We multiply parentheses ..

(+3x^2-51x+7x-119)-180=0

We get rid of parentheses

3x^2-51x+7x-119-180=0

We add all the numbers together, and all the variables

3x^2-44x-299=0

a = 3; b = -44; c = -299;
Δ = b2-4ac
Δ = -442-4·3·(-299)
Δ = 5524
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:

$\sqrt{\Delta}=\sqrt{5524}=\sqrt{4*1381}=\sqrt{4}*\sqrt{1381}=2\sqrt{1381}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-2\sqrt{1381}}{2*3}=\frac{44-2\sqrt{1381}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+2\sqrt{1381}}{2*3}=\frac{44+2\sqrt{1381}}{6}
$