(6x-9)(9x-5)=180

Solution for (6x-9)(9x-5)=180 equation:

(6x-9)(9x-5)=180

We move all terms to the left:

(6x-9)(9x-5)-(180)=0

We multiply parentheses ..

(+54x^2-30x-81x+45)-180=0

We get rid of parentheses

54x^2-30x-81x+45-180=0

We add all the numbers together, and all the variables

54x^2-111x-135=0

a = 54; b = -111; c = -135;
Δ = b2-4ac
Δ = -1112-4·54·(-135)
Δ = 41481
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:

$\sqrt{\Delta}=\sqrt{41481}=\sqrt{9*4609}=\sqrt{9}*\sqrt{4609}=3\sqrt{4609}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-111)-3\sqrt{4609}}{2*54}=\frac{111-3\sqrt{4609}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-111)+3\sqrt{4609}}{2*54}=\frac{111+3\sqrt{4609}}{108}
$