51/3m+71/4=-11/6m+30

Solution for 51/3m+71/4=-11/6m+30 equation:

51/3m+71/4=-11/6m+30

We move all terms to the left:

51/3m+71/4-(-11/6m+30)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 6m+30)!=0

m∈R


We get rid of parentheses

51/3m+11/6m-30+71/4=0

We calculate fractions


7668m^2/288m^2+4896m/288m^2+528m/288m^2-30=0

We multiply all the terms by the denominator


7668m^2+4896m+528m-30*288m^2=0

We add all the numbers together, and all the variables

7668m^2+5424m-30*288m^2=0

Wy multiply elements

7668m^2-8640m^2+5424m=0

We add all the numbers together, and all the variables

-972m^2+5424m=0

a = -972; b = 5424; c = 0;
Δ = b2-4ac
Δ = 54242-4·(-972)·0
Δ = 29419776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{29419776}=5424$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5424)-5424}{2*-972}=\frac{-10848}{-1944}
=5+47/81
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5424)+5424}{2*-972}=\frac{0}{-1944}
=0
$