-x(1-4x)=3x+8

Solution for -x(1-4x)=3x+8 equation:

-x(1-4x)=3x+8

We move all terms to the left:

-x(1-4x)-(3x+8)=0

We add all the numbers together, and all the variables

-x(-4x+1)-(3x+8)=0

We multiply parentheses

4x^2-x-(3x+8)=0

We get rid of parentheses

4x^2-x-3x-8=0

We add all the numbers together, and all the variables

4x^2-4x-8=0

a = 4; b = -4; c = -8;
Δ = b2-4ac
Δ = -42-4·4·(-8)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-12}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+12}{2*4}=\frac{16}{8}
=2
$