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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-12x^2+12x-(-2(x+1))=0


We calculate terms in parentheses: -(-2(x+1)), so:

-2(x+1)

We multiply parentheses

-2x-2

Back to the equation:

-(-2x-2)


We get rid of parentheses

-12x^2+12x+2x+2=0

We add all the numbers together, and all the variables

-12x^2+14x+2=0

a = -12; b = 14; c = +2;
Δ = b2-4ac
Δ = 142-4·(-12)·2
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{73}}{2*-12}=\frac{-14-2\sqrt{73}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{73}}{2*-12}=\frac{-14+2\sqrt{73}}{-24}
$