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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We add all the numbers together, and all the variables

-4x^2+7x+1=0

a = -4; b = 7; c = +1;
Δ = b2-4ac
Δ = 72-4·(-4)·1
Δ = 65
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{-(7)-\sqrt{65}}{2*-4}=\frac{-7-\sqrt{65}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{65}}{2*-4}=\frac{-7+\sqrt{65}}{-8}
$