1/3x+4/5x=7/6

Solution for 1/3x+4/5x=7/6 equation:

1/3x+4/5x=7/6

We move all terms to the left:

1/3x+4/5x-(7/6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x+4/5x-(+7/6)=0

We get rid of parentheses

1/3x+4/5x-7/6=0

We calculate fractions


(-525x^2)/540x^2+180x/540x^2+432x/540x^2=0

We multiply all the terms by the denominator


(-525x^2)+180x+432x=0

We add all the numbers together, and all the variables

(-525x^2)+612x=0

We get rid of parentheses

-525x^2+612x=0

a = -525; b = 612; c = 0;
Δ = b2-4ac
Δ = 6122-4·(-525)·0
Δ = 374544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{374544}=612$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(612)-612}{2*-525}=\frac{-1224}{-1050}
=1+29/175
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(612)+612}{2*-525}=\frac{0}{-1050}
=0
$