70/2x-3=99/x+1

Solution for 70/2x-3=99/x+1 equation:

70/2x-3=99/x+1

We move all terms to the left:

70/2x-3-(99/x+1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x+1)!=0

x∈R


We get rid of parentheses

70/2x-99/x-1-3=0

We calculate fractions


70x/2x^2+(-198x)/2x^2-1-3=0

We add all the numbers together, and all the variables

70x/2x^2+(-198x)/2x^2-4=0

We multiply all the terms by the denominator


70x+(-198x)-4*2x^2=0

Wy multiply elements

-8x^2+70x+(-198x)=0

We get rid of parentheses

-8x^2+70x-198x=0

We add all the numbers together, and all the variables

-8x^2-128x=0

a = -8; b = -128; c = 0;
Δ = b2-4ac
Δ = -1282-4·(-8)·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-128}{2*-8}=\frac{0}{-16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+128}{2*-8}=\frac{256}{-16}
=-16
$