(x-1)(4x-5)=5

Solution for (x-1)(4x-5)=5 equation:

(x-1)(4x-5)=5

We move all terms to the left:

(x-1)(4x-5)-(5)=0

We multiply parentheses ..

(+4x^2-5x-4x+5)-5=0

We get rid of parentheses

4x^2-5x-4x+5-5=0

We add all the numbers together, and all the variables

4x^2-9x=0

a = 4; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·4·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*4}=\frac{18}{8}
=2+1/4
$