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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

4x/2x^2+(-5x)/2x^2+15=0

We multiply all the terms by the denominator


4x+(-5x)+15*2x^2=0

Wy multiply elements

30x^2+4x+(-5x)=0

We get rid of parentheses

30x^2+4x-5x=0

We add all the numbers together, and all the variables

30x^2-1x=0

a = 30; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·30·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*30}=\frac{0}{60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*30}=\frac{2}{60}
=1/30
$