1/x+1/2x=1/90

Solution for 1/x+1/2x=1/90 equation:

1/x+1/2x=1/90

We move all terms to the left:

1/x+1/2x-(1/90)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/x+1/2x-(+1/90)=0

We get rid of parentheses

1/x+1/2x-1/90=0

We calculate fractions


(-4x^2)/1620x^2+1620x/1620x^2+810x/1620x^2=0

We multiply all the terms by the denominator


(-4x^2)+1620x+810x=0

We add all the numbers together, and all the variables

(-4x^2)+2430x=0

We get rid of parentheses

-4x^2+2430x=0

a = -4; b = 2430; c = 0;
Δ = b2-4ac
Δ = 24302-4·(-4)·0
Δ = 5904900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5904900}=2430$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2430)-2430}{2*-4}=\frac{-4860}{-8}
=607+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2430)+2430}{2*-4}=\frac{0}{-8}
=0
$