7/2x+7/9x=-17+25/6

Solution for 7/2x+7/9x=-17+25/6 equation:

7/2x+7/9x=-17+25/6

We move all terms to the left:

7/2x+7/9x-(-17+25/6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

7/2x+7/9x-(25/6-17)=0

We get rid of parentheses

7/2x+7/9x+17-25/6=0

We calculate fractions


(-4050x^2)/648x^2+2268x/648x^2+504x/648x^2+17=0

We multiply all the terms by the denominator


(-4050x^2)+2268x+504x+17*648x^2=0

We add all the numbers together, and all the variables

(-4050x^2)+2772x+17*648x^2=0

Wy multiply elements

(-4050x^2)+11016x^2+2772x=0

We get rid of parentheses

-4050x^2+11016x^2+2772x=0

We add all the numbers together, and all the variables

6966x^2+2772x=0

a = 6966; b = 2772; c = 0;
Δ = b2-4ac
Δ = 27722-4·6966·0
Δ = 7683984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7683984}=2772$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2772)-2772}{2*6966}=\frac{-5544}{13932}
=-154/387
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2772)+2772}{2*6966}=\frac{0}{13932}
=0
$