7/x-4+8/2x-8=5

Solution for 7/x-4+8/2x-8=5 equation:

7/x-4+8/2x-8=5

We move all terms to the left:

7/x-4+8/2x-8-(5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

7/x+8/2x-17=0

We calculate fractions


14x/2x^2+8x/2x^2-17=0

We multiply all the terms by the denominator


14x+8x-17*2x^2=0

We add all the numbers together, and all the variables

22x-17*2x^2=0

Wy multiply elements

-34x^2+22x=0

a = -34; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-34)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-34}=\frac{-44}{-68}
=11/17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-34}=\frac{0}{-68}
=0
$