180=(8x-41)(9x+17)

Solution for 180=(8x-41)(9x+17) equation:

180=(8x-41)(9x+17)

We move all terms to the left:

180-((8x-41)(9x+17))=0

We multiply parentheses ..

-((+72x^2+136x-369x-697))+180=0


We calculate terms in parentheses: -((+72x^2+136x-369x-697)), so:

(+72x^2+136x-369x-697)

We get rid of parentheses

72x^2+136x-369x-697

We add all the numbers together, and all the variables

72x^2-233x-697

Back to the equation:

-(72x^2-233x-697)


We get rid of parentheses

-72x^2+233x+697+180=0

We add all the numbers together, and all the variables

-72x^2+233x+877=0

a = -72; b = 233; c = +877;
Δ = b2-4ac
Δ = 2332-4·(-72)·877
Δ = 306865
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{-(233)-\sqrt{306865}}{2*-72}=\frac{-233-\sqrt{306865}}{-144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(233)+\sqrt{306865}}{2*-72}=\frac{-233+\sqrt{306865}}{-144}
$