1/3x-5/6=3/2x-9

Solution for 1/3x-5/6=3/2x-9 equation:

1/3x-5/6=3/2x-9

We move all terms to the left:

1/3x-5/6-(3/2x-9)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-9)!=0

x∈R


We get rid of parentheses

1/3x-3/2x+9-5/6=0

We calculate fractions


(-60x^2)/216x^2+72x/216x^2+(-324x)/216x^2+9=0

We multiply all the terms by the denominator


(-60x^2)+72x+(-324x)+9*216x^2=0

Wy multiply elements

(-60x^2)+1944x^2+72x+(-324x)=0

We get rid of parentheses

-60x^2+1944x^2+72x-324x=0

We add all the numbers together, and all the variables

1884x^2-252x=0

a = 1884; b = -252; c = 0;
Δ = b2-4ac
Δ = -2522-4·1884·0
Δ = 63504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63504}=252$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-252}{2*1884}=\frac{0}{3768}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+252}{2*1884}=\frac{504}{3768}
=21/157
$