1/9x+4/3=1/2x-1

Solution for 1/9x+4/3=1/2x-1 equation:

1/9x+4/3=1/2x-1

We move all terms to the left:

1/9x+4/3-(1/2x-1)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

1/9x-1/2x+1+4/3=0

We calculate fractions


144x^2/162x^2+18x/162x^2+(-81x)/162x^2+1=0

We multiply all the terms by the denominator


144x^2+18x+(-81x)+1*162x^2=0

Wy multiply elements

144x^2+162x^2+18x+(-81x)=0

We get rid of parentheses

144x^2+162x^2+18x-81x=0

We add all the numbers together, and all the variables

306x^2-63x=0

a = 306; b = -63; c = 0;
Δ = b2-4ac
Δ = -632-4·306·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-63}{2*306}=\frac{0}{612}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+63}{2*306}=\frac{126}{612}
=7/34
$