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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5x^2+x-5=0

a = 5; b = 1; c = -5;
Δ = b2-4ac
Δ = 12-4·5·(-5)
Δ = 101
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{-(1)-\sqrt{101}}{2*5}=\frac{-1-\sqrt{101}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{101}}{2*5}=\frac{-1+\sqrt{101}}{10}
$