1/5x+1/9x+1/5=37/45

Solution for 1/5x+1/9x+1/5=37/45 equation:

1/5x+1/9x+1/5=37/45

We move all terms to the left:

1/5x+1/9x+1/5-(37/45)=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+1/5-(+37/45)=0

We get rid of parentheses

1/5x+1/9x+1/5-37/45=0

We calculate fractions


(-74925x^2)/50625x^2+1620x/50625x^2+5625x/50625x^2+1620x/50625x^2=0

We multiply all the terms by the denominator


(-74925x^2)+1620x+5625x+1620x=0

We add all the numbers together, and all the variables

(-74925x^2)+8865x=0

We get rid of parentheses

-74925x^2+8865x=0

a = -74925; b = 8865; c = 0;
Δ = b2-4ac
Δ = 88652-4·(-74925)·0
Δ = 78588225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{78588225}=8865$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8865)-8865}{2*-74925}=\frac{-17730}{-149850}
=197/1665
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8865)+8865}{2*-74925}=\frac{0}{-149850}
=0
$