-1/5x-1/9x=-102

Solution for -1/5x-1/9x=-102 equation:

-1/5x-1/9x=-102

We move all terms to the left:

-1/5x-1/9x-(-102)=0


Domain of the equation: 5x!=0

x!=0/5

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

-1/5x-1/9x+102=0

We calculate fractions


(-9x)/45x^2+(-5x)/45x^2+102=0

We multiply all the terms by the denominator


(-9x)+(-5x)+102*45x^2=0

Wy multiply elements

4590x^2+(-9x)+(-5x)=0

We get rid of parentheses

4590x^2-9x-5x=0

We add all the numbers together, and all the variables

4590x^2-14x=0

a = 4590; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·4590·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*4590}=\frac{0}{9180}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*4590}=\frac{28}{9180}
=7/2295
$