(1/7)m-(4/7)=3

Solution for (1/7)m-(4/7)=3 equation:

(1/7)m-(4/7)=3

We move all terms to the left:

(1/7)m-(4/7)-(3)=0


Domain of the equation: 7)m!=0

m!=0/1

m!=0

m∈R


determiningTheFunctionDomain
(1/7)m-3-(4/7)=0

We add all the numbers together, and all the variables

(+1/7)m-3-(+4/7)=0

We multiply parentheses

m^2-3-(+4/7)=0

We get rid of parentheses

m^2-3-4/7=0

We multiply all the terms by the denominator


m^2*7-4-3*7=0

We add all the numbers together, and all the variables

m^2*7-25=0

Wy multiply elements

7m^2-25=0

a = 7; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·7·(-25)
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{7}}{2*7}=\frac{0-10\sqrt{7}}{14}
=-\frac{10\sqrt{7}}{14}
=-\frac{5\sqrt{7}}{7}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{7}}{2*7}=\frac{0+10\sqrt{7}}{14}
=\frac{10\sqrt{7}}{14}
=\frac{5\sqrt{7}}{7}
$