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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-180x^2)/432x^2+324x/432x^2+(-144x)/432x^2+5=0

We multiply all the terms by the denominator


(-180x^2)+324x+(-144x)+5*432x^2=0

Wy multiply elements

(-180x^2)+2160x^2+324x+(-144x)=0

We get rid of parentheses

-180x^2+2160x^2+324x-144x=0

We add all the numbers together, and all the variables

1980x^2+180x=0

a = 1980; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·1980·0
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*1980}=\frac{-360}{3960}
=-1/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*1980}=\frac{0}{3960}
=0
$