1/2x-8-3/x-4=5

Solution for 1/2x-8-3/x-4=5 equation:

1/2x-8-3/x-4=5

We move all terms to the left:

1/2x-8-3/x-4-(5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-3/x-17=0

We calculate fractions


x/2x^2+(-6x)/2x^2-17=0

We multiply all the terms by the denominator


x+(-6x)-17*2x^2=0

Wy multiply elements

-34x^2+x+(-6x)=0

We get rid of parentheses

-34x^2+x-6x=0

We add all the numbers together, and all the variables

-34x^2-5x=0

a = -34; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-34)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-34}=\frac{0}{-68}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-34}=\frac{10}{-68}
=-5/34
$