5/6m+14=9/4m-20

Solution for 5/6m+14=9/4m-20 equation:

5/6m+14=9/4m-20

We move all terms to the left:

5/6m+14-(9/4m-20)=0


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R



Domain of the equation: 4m-20)!=0

m∈R


We get rid of parentheses

5/6m-9/4m+20+14=0

We calculate fractions


20m/24m^2+(-54m)/24m^2+20+14=0

We add all the numbers together, and all the variables

20m/24m^2+(-54m)/24m^2+34=0

We multiply all the terms by the denominator


20m+(-54m)+34*24m^2=0

Wy multiply elements

816m^2+20m+(-54m)=0

We get rid of parentheses

816m^2+20m-54m=0

We add all the numbers together, and all the variables

816m^2-34m=0

a = 816; b = -34; c = 0;
Δ = b2-4ac
Δ = -342-4·816·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-34}{2*816}=\frac{0}{1632}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+34}{2*816}=\frac{68}{1632}
=1/24
$