5/18x+16=10-2/9x

Solution for 5/18x+16=10-2/9x equation:

5/18x+16=10-2/9x

We move all terms to the left:

5/18x+16-(10-2/9x)=0


Domain of the equation: 18x!=0

x!=0/18

x!=0

x∈R



Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/18x-(-2/9x+10)+16=0

We get rid of parentheses

5/18x+2/9x-10+16=0

We calculate fractions


45x/162x^2+36x/162x^2-10+16=0

We add all the numbers together, and all the variables

45x/162x^2+36x/162x^2+6=0

We multiply all the terms by the denominator


45x+36x+6*162x^2=0

We add all the numbers together, and all the variables

81x+6*162x^2=0

Wy multiply elements

972x^2+81x=0

a = 972; b = 81; c = 0;
Δ = b2-4ac
Δ = 812-4·972·0
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-81}{2*972}=\frac{-162}{1944}
=-1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+81}{2*972}=\frac{0}{1944}
=0
$