5(1-X)+3(1+X)/(1-2x)=8

Solution for 5(1-X)+3(1+X)/(1-2x)=8 equation:

5(1-X)+3(1+X)/(1-2X)=8

We move all terms to the left:

5(1-X)+3(1+X)/(1-2X)-(8)=0


Domain of the equation: (1-2X)!=0

We move all terms containing X to the left, all other terms to the right

-2X!=-1

X!=-1/-2

X!=1/2

X∈R


We add all the numbers together, and all the variables

5(-1X+1)+3(X+1)/(-2X+1)-8=0

We multiply parentheses

-5X+3(X+1)/(-2X+1)+5-8=0

We multiply all the terms by the denominator


-5X*(-2X+1)+3(X+1)+5*(-2X+1)-8*(-2X+1)=0

We multiply parentheses

10X^2-5X+3X-10X+16X+3+5-8=0

We add all the numbers together, and all the variables

10X^2+4X=0

a = 10; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·10·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*10}=\frac{-8}{20}
=-2/5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*10}=\frac{0}{20}
=0
$