(9x+25)(13x-19)=180

Solution for (9x+25)(13x-19)=180 equation:

(9x+25)(13x-19)=180

We move all terms to the left:

(9x+25)(13x-19)-(180)=0

We multiply parentheses ..

(+117x^2-171x+325x-475)-180=0

We get rid of parentheses

117x^2-171x+325x-475-180=0

We add all the numbers together, and all the variables

117x^2+154x-655=0

a = 117; b = 154; c = -655;
Δ = b2-4ac
Δ = 1542-4·117·(-655)
Δ = 330256
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:

$\sqrt{\Delta}=\sqrt{330256}=\sqrt{16*20641}=\sqrt{16}*\sqrt{20641}=4\sqrt{20641}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(154)-4\sqrt{20641}}{2*117}=\frac{-154-4\sqrt{20641}}{234}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(154)+4\sqrt{20641}}{2*117}=\frac{-154+4\sqrt{20641}}{234}
$