(13/3)m=38/7

Solution for (13/3)m=38/7 equation:

(13/3)m=38/7

We move all terms to the left:

(13/3)m-(38/7)=0


Domain of the equation: 3)m!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

(+13/3)m-(+38/7)=0

We multiply parentheses

13m^2-(+38/7)=0

We get rid of parentheses

13m^2-38/7=0

We multiply all the terms by the denominator


13m^2*7-38=0

Wy multiply elements

91m^2-38=0

a = 91; b = 0; c = -38;
Δ = b2-4ac
Δ = 02-4·91·(-38)
Δ = 13832
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:

$\sqrt{\Delta}=\sqrt{13832}=\sqrt{4*3458}=\sqrt{4}*\sqrt{3458}=2\sqrt{3458}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3458}}{2*91}=\frac{0-2\sqrt{3458}}{182}
=-\frac{2\sqrt{3458}}{182}
=-\frac{\sqrt{3458}}{91}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3458}}{2*91}=\frac{0+2\sqrt{3458}}{182}
=\frac{2\sqrt{3458}}{182}
=\frac{\sqrt{3458}}{91}
$