(8x+1)(9x-4)=180

Solution for (8x+1)(9x-4)=180 equation:

(8x+1)(9x-4)=180

We move all terms to the left:

(8x+1)(9x-4)-(180)=0

We multiply parentheses ..

(+72x^2-32x+9x-4)-180=0

We get rid of parentheses

72x^2-32x+9x-4-180=0

We add all the numbers together, and all the variables

72x^2-23x-184=0

a = 72; b = -23; c = -184;
Δ = b2-4ac
Δ = -232-4·72·(-184)
Δ = 53521
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{-(-23)-\sqrt{53521}}{2*72}=\frac{23-\sqrt{53521}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{53521}}{2*72}=\frac{23+\sqrt{53521}}{144}
$