35/2x+2=14/7x-9

Solution for 35/2x+2=14/7x-9 equation:

35/2x+2=14/7x-9

We move all terms to the left:

35/2x+2-(14/7x-9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 7x-9)!=0

x∈R


We get rid of parentheses

35/2x-14/7x+9+2=0

We calculate fractions


245x/14x^2+(-28x)/14x^2+9+2=0

We add all the numbers together, and all the variables

245x/14x^2+(-28x)/14x^2+11=0

We multiply all the terms by the denominator


245x+(-28x)+11*14x^2=0

Wy multiply elements

154x^2+245x+(-28x)=0

We get rid of parentheses

154x^2+245x-28x=0

We add all the numbers together, and all the variables

154x^2+217x=0

a = 154; b = 217; c = 0;
Δ = b2-4ac
Δ = 2172-4·154·0
Δ = 47089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{47089}=217$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(217)-217}{2*154}=\frac{-434}{308}
=-1+9/22
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(217)+217}{2*154}=\frac{0}{308}
=0
$