4/5x-1/3x=-14

Solution for 4/5x-1/3x=-14 equation:

4/5x-1/3x=-14

We move all terms to the left:

4/5x-1/3x-(-14)=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+14=0

We calculate fractions


12x/15x^2+(-5x)/15x^2+14=0

We multiply all the terms by the denominator


12x+(-5x)+14*15x^2=0

Wy multiply elements

210x^2+12x+(-5x)=0

We get rid of parentheses

210x^2+12x-5x=0

We add all the numbers together, and all the variables

210x^2+7x=0

a = 210; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·210·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*210}=\frac{-14}{420}
=-1/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*210}=\frac{0}{420}
=0
$