180=(6x-1)(5x+17)

Solution for 180=(6x-1)(5x+17) equation:

180=(6x-1)(5x+17)

We move all terms to the left:

180-((6x-1)(5x+17))=0

We multiply parentheses ..

-((+30x^2+102x-5x-17))+180=0


We calculate terms in parentheses: -((+30x^2+102x-5x-17)), so:

(+30x^2+102x-5x-17)

We get rid of parentheses

30x^2+102x-5x-17

We add all the numbers together, and all the variables

30x^2+97x-17

Back to the equation:

-(30x^2+97x-17)


We get rid of parentheses

-30x^2-97x+17+180=0

We add all the numbers together, and all the variables

-30x^2-97x+197=0

a = -30; b = -97; c = +197;
Δ = b2-4ac
Δ = -972-4·(-30)·197
Δ = 33049
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{-(-97)-\sqrt{33049}}{2*-30}=\frac{97-\sqrt{33049}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-97)+\sqrt{33049}}{2*-30}=\frac{97+\sqrt{33049}}{-60}
$