5(1-x)7x=6(-1-x)

Solution for 5(1-x)7x=6(-1-x) equation:

5(1-x)7x=6(-1-x)

We move all terms to the left:

5(1-x)7x-(6(-1-x))=0

We add all the numbers together, and all the variables

5(-1x+1)7x-(6(-1x-1))=0

We multiply parentheses

-35x^2+35x-(6(-1x-1))=0


We calculate terms in parentheses: -(6(-1x-1)), so:

6(-1x-1)

We multiply parentheses

-6x-6

Back to the equation:

-(-6x-6)


We get rid of parentheses

-35x^2+35x+6x+6=0

We add all the numbers together, and all the variables

-35x^2+41x+6=0

a = -35; b = 41; c = +6;
Δ = b2-4ac
Δ = 412-4·(-35)·6
Δ = 2521
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{-(41)-\sqrt{2521}}{2*-35}=\frac{-41-\sqrt{2521}}{-70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+\sqrt{2521}}{2*-35}=\frac{-41+\sqrt{2521}}{-70}
$