1/9x+3=3/10x-6

Solution for 1/9x+3=3/10x-6 equation:

1/9x+3=3/10x-6

We move all terms to the left:

1/9x+3-(3/10x-6)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 10x-6)!=0

x∈R


We get rid of parentheses

1/9x-3/10x+6+3=0

We calculate fractions


10x/90x^2+(-27x)/90x^2+6+3=0

We add all the numbers together, and all the variables

10x/90x^2+(-27x)/90x^2+9=0

We multiply all the terms by the denominator


10x+(-27x)+9*90x^2=0

Wy multiply elements

810x^2+10x+(-27x)=0

We get rid of parentheses

810x^2+10x-27x=0

We add all the numbers together, and all the variables

810x^2-17x=0

a = 810; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·810·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*810}=\frac{0}{1620}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*810}=\frac{34}{1620}
=17/810
$