(5x-3)(4x-2)=180

Solution for (5x-3)(4x-2)=180 equation:

(5x-3)(4x-2)=180

We move all terms to the left:

(5x-3)(4x-2)-(180)=0

We multiply parentheses ..

(+20x^2-10x-12x+6)-180=0

We get rid of parentheses

20x^2-10x-12x+6-180=0

We add all the numbers together, and all the variables

20x^2-22x-174=0

a = 20; b = -22; c = -174;
Δ = b2-4ac
Δ = -222-4·20·(-174)
Δ = 14404
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:

$\sqrt{\Delta}=\sqrt{14404}=\sqrt{4*3601}=\sqrt{4}*\sqrt{3601}=2\sqrt{3601}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{3601}}{2*20}=\frac{22-2\sqrt{3601}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{3601}}{2*20}=\frac{22+2\sqrt{3601}}{40}
$