3/7x-5=1/2x+9

Solution for 3/7x-5=1/2x+9 equation:

3/7x-5=1/2x+9

We move all terms to the left:

3/7x-5-(1/2x+9)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 2x+9)!=0

x∈R


We get rid of parentheses

3/7x-1/2x-9-5=0

We calculate fractions


6x/14x^2+(-7x)/14x^2-9-5=0

We add all the numbers together, and all the variables

6x/14x^2+(-7x)/14x^2-14=0

We multiply all the terms by the denominator


6x+(-7x)-14*14x^2=0

Wy multiply elements

-196x^2+6x+(-7x)=0

We get rid of parentheses

-196x^2+6x-7x=0

We add all the numbers together, and all the variables

-196x^2-1x=0

a = -196; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-196)·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*-196}=\frac{0}{-392}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-196}=\frac{2}{-392}
=-1/196
$