(x-1)(5x=4)

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

(x-1)(5x=4)

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5x^2-9x+4=0

a = 5; b = -9; c = +4;
Δ = b2-4ac
Δ = -92-4·5·4
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*5}=\frac{8}{10}
=4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+1}{2*5}=\frac{10}{10}
=1
$