9/7x+2=1/2x+13

Solution for 9/7x+2=1/2x+13 equation:

9/7x+2=1/2x+13

We move all terms to the left:

9/7x+2-(1/2x+13)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 2x+13)!=0

x∈R


We get rid of parentheses

9/7x-1/2x-13+2=0

We calculate fractions


18x/14x^2+(-7x)/14x^2-13+2=0

We add all the numbers together, and all the variables

18x/14x^2+(-7x)/14x^2-11=0

We multiply all the terms by the denominator


18x+(-7x)-11*14x^2=0

Wy multiply elements

-154x^2+18x+(-7x)=0

We get rid of parentheses

-154x^2+18x-7x=0

We add all the numbers together, and all the variables

-154x^2+11x=0

a = -154; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-154)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-154}=\frac{-22}{-308}
=1/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-154}=\frac{0}{-308}
=0
$