-5x(x-1)-x+1=-18

Solution for -5x(x-1)-x+1=-18 equation:

-5x(x-1)-x+1=-18

We move all terms to the left:

-5x(x-1)-x+1-(-18)=0

We add all the numbers together, and all the variables

-1x-5x(x-1)+19=0

We multiply parentheses

-5x^2-1x+5x+19=0

We add all the numbers together, and all the variables

-5x^2+4x+19=0

a = -5; b = 4; c = +19;
Δ = b2-4ac
Δ = 42-4·(-5)·19
Δ = 396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6\sqrt{11}}{2*-5}=\frac{-4-6\sqrt{11}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6\sqrt{11}}{2*-5}=\frac{-4+6\sqrt{11}}{-10}
$