4/5x-1/3x=7/30

Solution for 4/5x-1/3x=7/30 equation:

4/5x-1/3x=7/30

We move all terms to the left:

4/5x-1/3x-(7/30)=0


Domain of the equation: 5x!=0

x!=0/5

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

4/5x-1/3x-(+7/30)=0

We get rid of parentheses

4/5x-1/3x-7/30=0

We calculate fractions


(-315x^2)/1350x^2+1080x/1350x^2+(-450x)/1350x^2=0

We multiply all the terms by the denominator


(-315x^2)+1080x+(-450x)=0

We get rid of parentheses

-315x^2+1080x-450x=0

We add all the numbers together, and all the variables

-315x^2+630x=0

a = -315; b = 630; c = 0;
Δ = b2-4ac
Δ = 6302-4·(-315)·0
Δ = 396900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{396900}=630$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(630)-630}{2*-315}=\frac{-1260}{-630}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(630)+630}{2*-315}=\frac{0}{-630}
=0
$