(x-2)(5x-4)+1=0

Solution for (x-2)(5x-4)+1=0 equation:

(x-2)(5x-4)+1=0

We multiply parentheses ..

(+5x^2-4x-10x+8)+1=0

We get rid of parentheses

5x^2-4x-10x+8+1=0

We add all the numbers together, and all the variables

5x^2-14x+9=0

a = 5; b = -14; c = +9;
Δ = b2-4ac
Δ = -142-4·5·9
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4}{2*5}=\frac{10}{10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4}{2*5}=\frac{18}{10}
=1+4/5
$