3/7*m=6

Solution for 3/7*m=6 equation:

3/7*m=6

We move all terms to the left:

3/7*m-(6)=0


Domain of the equation: 7*m!=0

m!=0/1

m!=0

m∈R


We multiply all the terms by the denominator


-6*7*m+3=0

Wy multiply elements

-42m*m+3=0

Wy multiply elements

-42m^2+3=0

a = -42; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-42)·3
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{14}}{2*-42}=\frac{0-6\sqrt{14}}{-84}
=-\frac{6\sqrt{14}}{-84}
=-\frac{\sqrt{14}}{-14}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{14}}{2*-42}=\frac{0+6\sqrt{14}}{-84}
=\frac{6\sqrt{14}}{-84}
=\frac{\sqrt{14}}{-14}
$