(5/6)m-(2/3)=14

Solution for (5/6)m-(2/3)=14 equation:

(5/6)m-(2/3)=14

We move all terms to the left:

(5/6)m-(2/3)-(14)=0


Domain of the equation: 6)m!=0

m!=0/1

m!=0

m∈R


determiningTheFunctionDomain
(5/6)m-14-(2/3)=0

We add all the numbers together, and all the variables

(+5/6)m-14-(+2/3)=0

We multiply parentheses

5m^2-14-(+2/3)=0

We get rid of parentheses

5m^2-14-2/3=0

We multiply all the terms by the denominator


5m^2*3-2-14*3=0

We add all the numbers together, and all the variables

5m^2*3-44=0

Wy multiply elements

15m^2-44=0

a = 15; b = 0; c = -44;
Δ = b2-4ac
Δ = 02-4·15·(-44)
Δ = 2640
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2640}=\sqrt{16*165}=\sqrt{16}*\sqrt{165}=4\sqrt{165}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{165}}{2*15}=\frac{0-4\sqrt{165}}{30}
=-\frac{4\sqrt{165}}{30}
=-\frac{2\sqrt{165}}{15}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{165}}{2*15}=\frac{0+4\sqrt{165}}{30}
=\frac{4\sqrt{165}}{30}
=\frac{2\sqrt{165}}{15}
$