25/3x-10/6=-4/9x

Solution for 25/3x-10/6=-4/9x equation:

25/3x-10/6=-4/9x

We move all terms to the left:

25/3x-10/6-(-4/9x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

25/3x+4/9x-10/6=0

We calculate fractions


(-2430x^2)/972x^2+8100x/972x^2+432x/972x^2=0

We multiply all the terms by the denominator


(-2430x^2)+8100x+432x=0

We add all the numbers together, and all the variables

(-2430x^2)+8532x=0

We get rid of parentheses

-2430x^2+8532x=0

a = -2430; b = 8532; c = 0;
Δ = b2-4ac
Δ = 85322-4·(-2430)·0
Δ = 72795024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{72795024}=8532$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8532)-8532}{2*-2430}=\frac{-17064}{-4860}
=3+23/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8532)+8532}{2*-2430}=\frac{0}{-4860}
=0
$