5/9x-5/3=3/4x-12

Solution for 5/9x-5/3=3/4x-12 equation:

5/9x-5/3=3/4x-12

We move all terms to the left:

5/9x-5/3-(3/4x-12)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 4x-12)!=0

x∈R


We get rid of parentheses

5/9x-3/4x+12-5/3=0

We calculate fractions


(-720x^2)/324x^2+180x/324x^2+(-243x)/324x^2+12=0

We multiply all the terms by the denominator


(-720x^2)+180x+(-243x)+12*324x^2=0

Wy multiply elements

(-720x^2)+3888x^2+180x+(-243x)=0

We get rid of parentheses

-720x^2+3888x^2+180x-243x=0

We add all the numbers together, and all the variables

3168x^2-63x=0

a = 3168; b = -63; c = 0;
Δ = b2-4ac
Δ = -632-4·3168·0
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*3168}=\frac{0}{6336}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+63}{2*3168}=\frac{126}{6336}
=7/352
$