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

Solution for (4x-5)(x-1)=0 equation:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-9x+5=0

a = 4; b = -9; c = +5;
Δ = b2-4ac
Δ = -92-4·4·5
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-1}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+1}{2*4}=\frac{10}{8}
=1+1/4
$