7/2x+7/9x=-17+25/16

Solution for 7/2x+7/9x=-17+25/16 equation:

7/2x+7/9x=-17+25/16

We move all terms to the left:

7/2x+7/9x-(-17+25/16)=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-(25/16-17)=0

We get rid of parentheses

7/2x+7/9x+17-25/16=0

We calculate fractions


(-4050x^2)/288x^2+1008x/288x^2+224x/288x^2+17=0

We multiply all the terms by the denominator


(-4050x^2)+1008x+224x+17*288x^2=0

We add all the numbers together, and all the variables

(-4050x^2)+1232x+17*288x^2=0

Wy multiply elements

(-4050x^2)+4896x^2+1232x=0

We get rid of parentheses

-4050x^2+4896x^2+1232x=0

We add all the numbers together, and all the variables

846x^2+1232x=0

a = 846; b = 1232; c = 0;
Δ = b2-4ac
Δ = 12322-4·846·0
Δ = 1517824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1517824}=1232$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1232)-1232}{2*846}=\frac{-2464}{1692}
=-1+193/423
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1232)+1232}{2*846}=\frac{0}{1692}
=0
$