4(1-x)2x=-3(x+1)

Solution for 4(1-x)2x=-3(x+1) equation:

4(1-x)2x=-3(x+1)

We move all terms to the left:

4(1-x)2x-(-3(x+1))=0

We add all the numbers together, and all the variables

4(-1x+1)2x-(-3(x+1))=0

We multiply parentheses

-8x^2+8x-(-3(x+1))=0


We calculate terms in parentheses: -(-3(x+1)), so:

-3(x+1)

We multiply parentheses

-3x-3

Back to the equation:

-(-3x-3)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-8x^2+11x+3=0

a = -8; b = 11; c = +3;
Δ = b2-4ac
Δ = 112-4·(-8)·3
Δ = 217
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{-(11)-\sqrt{217}}{2*-8}=\frac{-11-\sqrt{217}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{217}}{2*-8}=\frac{-11+\sqrt{217}}{-16}
$