1/2x+9+2/7x=30/7

Solution for 1/2x+9+2/7x=30/7 equation:

1/2x+9+2/7x=30/7

We move all terms to the left:

1/2x+9+2/7x-(30/7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+2/7x+9-(+30/7)=0

We get rid of parentheses

1/2x+2/7x+9-30/7=0

We calculate fractions


343x/686x^2+4x/686x^2+(-60x)/686x^2+9=0

We multiply all the terms by the denominator


343x+4x+(-60x)+9*686x^2=0

We add all the numbers together, and all the variables

347x+(-60x)+9*686x^2=0

Wy multiply elements

6174x^2+347x+(-60x)=0

We get rid of parentheses

6174x^2+347x-60x=0

We add all the numbers together, and all the variables

6174x^2+287x=0

a = 6174; b = 287; c = 0;
Δ = b2-4ac
Δ = 2872-4·6174·0
Δ = 82369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{82369}=287$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(287)-287}{2*6174}=\frac{-574}{12348}
=-41/882
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(287)+287}{2*6174}=\frac{0}{12348}
=0
$