(3x-4)(5x-6)=180

Solution for (3x-4)(5x-6)=180 equation:

(3x-4)(5x-6)=180

We move all terms to the left:

(3x-4)(5x-6)-(180)=0

We multiply parentheses ..

(+15x^2-18x-20x+24)-180=0

We get rid of parentheses

15x^2-18x-20x+24-180=0

We add all the numbers together, and all the variables

15x^2-38x-156=0

a = 15; b = -38; c = -156;
Δ = b2-4ac
Δ = -382-4·15·(-156)
Δ = 10804
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:

$\sqrt{\Delta}=\sqrt{10804}=\sqrt{4*2701}=\sqrt{4}*\sqrt{2701}=2\sqrt{2701}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{2701}}{2*15}=\frac{38-2\sqrt{2701}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{2701}}{2*15}=\frac{38+2\sqrt{2701}}{30}
$