(2x-10)(4x-2)=x-1-1

Solution for (2x-10)(4x-2)=x-1-1 equation:

(2x-10)(4x-2)=x-1-1

We move all terms to the left:

(2x-10)(4x-2)-(x-1-1)=0

We add all the numbers together, and all the variables

(2x-10)(4x-2)-(x-2)=0

We get rid of parentheses

(2x-10)(4x-2)-x+2=0

We multiply parentheses ..

(+8x^2-4x-40x+20)-x+2=0

We add all the numbers together, and all the variables

(+8x^2-4x-40x+20)-1x+2=0

We get rid of parentheses

8x^2-4x-40x-1x+20+2=0

We add all the numbers together, and all the variables

8x^2-45x+22=0

a = 8; b = -45; c = +22;
Δ = b2-4ac
Δ = -452-4·8·22
Δ = 1321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{1321}}{2*8}=\frac{45-\sqrt{1321}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{1321}}{2*8}=\frac{45+\sqrt{1321}}{16}
$