4/5m-1/3m=14

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

4/5m-1/3m=14

We move all terms to the left:

4/5m-1/3m-(14)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R



Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-210m^2+7m=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:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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