8/x+10=4/2x-7

Solution for 8/x+10=4/2x-7 equation:

8/x+10=4/2x-7

We move all terms to the left:

8/x+10-(4/2x-7)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-7)!=0

x∈R


We get rid of parentheses

8/x-4/2x+7+10=0

We calculate fractions


16x/2x^2+(-4x)/2x^2+7+10=0

We add all the numbers together, and all the variables

16x/2x^2+(-4x)/2x^2+17=0

We multiply all the terms by the denominator


16x+(-4x)+17*2x^2=0

Wy multiply elements

34x^2+16x+(-4x)=0

We get rid of parentheses

34x^2+16x-4x=0

We add all the numbers together, and all the variables

34x^2+12x=0

a = 34; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·34·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*34}=\frac{-24}{68}
=-6/17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*34}=\frac{0}{68}
=0
$