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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-4x^2+2x+4x-(-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 add all the numbers together, and all the variables

-4x^2+6x-(-3x-3)=0

We get rid of parentheses

-4x^2+6x+3x+3=0

We add all the numbers together, and all the variables

-4x^2+9x+3=0

a = -4; b = 9; c = +3;
Δ = b2-4ac
Δ = 92-4·(-4)·3
Δ = 129
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{-(9)-\sqrt{129}}{2*-4}=\frac{-9-\sqrt{129}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{129}}{2*-4}=\frac{-9+\sqrt{129}}{-8}
$