(4/5)m=13/21

Solution for (4/5)m=13/21 equation:

(4/5)m=13/21

We move all terms to the left:

(4/5)m-(13/21)=0


Domain of the equation: 5)m!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

(+4/5)m-(+13/21)=0

We multiply parentheses

4m^2-(+13/21)=0

We get rid of parentheses

4m^2-13/21=0

We multiply all the terms by the denominator


4m^2*21-13=0

Wy multiply elements

84m^2-13=0

a = 84; b = 0; c = -13;
Δ = b2-4ac
Δ = 02-4·84·(-13)
Δ = 4368
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:

$\sqrt{\Delta}=\sqrt{4368}=\sqrt{16*273}=\sqrt{16}*\sqrt{273}=4\sqrt{273}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{273}}{2*84}=\frac{0-4\sqrt{273}}{168}
=-\frac{4\sqrt{273}}{168}
=-\frac{\sqrt{273}}{42}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{273}}{2*84}=\frac{0+4\sqrt{273}}{168}
=\frac{4\sqrt{273}}{168}
=\frac{\sqrt{273}}{42}
$