x/3x+10=9x-12

Solution for x/3x+10=9x-12 equation:

x/3x+10=9x-12

We move all terms to the left:

x/3x+10-(9x-12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

x/3x-9x+12+10=0

We multiply all the terms by the denominator


x-9x*3x+12*3x+10*3x=0

Wy multiply elements

-27x^2+x+36x+30x=0

We add all the numbers together, and all the variables

-27x^2+67x=0

a = -27; b = 67; c = 0;
Δ = b2-4ac
Δ = 672-4·(-27)·0
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(67)-67}{2*-27}=\frac{-134}{-54}
=2+13/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(67)+67}{2*-27}=\frac{0}{-54}
=0
$