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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


140x/2x^2+(-99x)/2x^2+3+1=0

We add all the numbers together, and all the variables

140x/2x^2+(-99x)/2x^2+4=0

We multiply all the terms by the denominator


140x+(-99x)+4*2x^2=0

Wy multiply elements

8x^2+140x+(-99x)=0

We get rid of parentheses

8x^2+140x-99x=0

We add all the numbers together, and all the variables

8x^2+41x=0

a = 8; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·8·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*8}=\frac{-82}{16}
=-5+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*8}=\frac{0}{16}
=0
$