(9x-25)(8x-6)=180

Solution for (9x-25)(8x-6)=180 equation:

(9x-25)(8x-6)=180

We move all terms to the left:

(9x-25)(8x-6)-(180)=0

We multiply parentheses ..

(+72x^2-54x-200x+150)-180=0

We get rid of parentheses

72x^2-54x-200x+150-180=0

We add all the numbers together, and all the variables

72x^2-254x-30=0

a = 72; b = -254; c = -30;
Δ = b2-4ac
Δ = -2542-4·72·(-30)
Δ = 73156
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:

$\sqrt{\Delta}=\sqrt{73156}=\sqrt{4*18289}=\sqrt{4}*\sqrt{18289}=2\sqrt{18289}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-254)-2\sqrt{18289}}{2*72}=\frac{254-2\sqrt{18289}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-254)+2\sqrt{18289}}{2*72}=\frac{254+2\sqrt{18289}}{144}
$