(4x-1)(2x-1)=180

Solution for (4x-1)(2x-1)=180 equation:

(4x-1)(2x-1)=180

We move all terms to the left:

(4x-1)(2x-1)-(180)=0

We multiply parentheses ..

(+8x^2-4x-2x+1)-180=0

We get rid of parentheses

8x^2-4x-2x+1-180=0

We add all the numbers together, and all the variables

8x^2-6x-179=0

a = 8; b = -6; c = -179;
Δ = b2-4ac
Δ = -62-4·8·(-179)
Δ = 5764
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:

$\sqrt{\Delta}=\sqrt{5764}=\sqrt{4*1441}=\sqrt{4}*\sqrt{1441}=2\sqrt{1441}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{1441}}{2*8}=\frac{6-2\sqrt{1441}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{1441}}{2*8}=\frac{6+2\sqrt{1441}}{16}
$