1/3x+5/6=3/4x-3

Solution for 1/3x+5/6=3/4x-3 equation:

1/3x+5/6=3/4x-3

We move all terms to the left:

1/3x+5/6-(3/4x-3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x-3)!=0

x∈R


We get rid of parentheses

1/3x-3/4x+3+5/6=0

We calculate fractions


240x^2/432x^2+144x/432x^2+(-324x)/432x^2+3=0

We multiply all the terms by the denominator


240x^2+144x+(-324x)+3*432x^2=0

Wy multiply elements

240x^2+1296x^2+144x+(-324x)=0

We get rid of parentheses

240x^2+1296x^2+144x-324x=0

We add all the numbers together, and all the variables

1536x^2-180x=0

a = 1536; b = -180; c = 0;
Δ = b2-4ac
Δ = -1802-4·1536·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-180}{2*1536}=\frac{0}{3072}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+180}{2*1536}=\frac{360}{3072}
=15/128
$