2/x-7=8/5x+10

Solution for 2/x-7=8/5x+10 equation:

2/x-7=8/5x+10

We move all terms to the left:

2/x-7-(8/5x+10)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x+10)!=0

x∈R


We get rid of parentheses

2/x-8/5x-10-7=0

We calculate fractions


10x/5x^2+(-8x)/5x^2-10-7=0

We add all the numbers together, and all the variables

10x/5x^2+(-8x)/5x^2-17=0

We multiply all the terms by the denominator


10x+(-8x)-17*5x^2=0

Wy multiply elements

-85x^2+10x+(-8x)=0

We get rid of parentheses

-85x^2+10x-8x=0

We add all the numbers together, and all the variables

-85x^2+2x=0

a = -85; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-85)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-85}=\frac{-4}{-170}
=2/85
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-85}=\frac{0}{-170}
=0
$