((36)/(9))=(1)/(3)m(2)-10

Solution for ((36)/(9))=(1)/(3)m(2)-10 equation:

((36)/(9))=(1)/(3)m(2)-10

We move all terms to the left:

((36)/(9))-((1)/(3)m(2)-10)=0


Domain of the equation: 3m2-10)!=0

m∈R


We add all the numbers together, and all the variables

-(1/3m2-10)+4=0

We get rid of parentheses

-1/3m2+10+4=0

We multiply all the terms by the denominator


10*3m2+4*3m2-1=0

Wy multiply elements

30m^2+12m^2-1=0

We add all the numbers together, and all the variables

42m^2-1=0

a = 42; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·42·(-1)
Δ = 168
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:

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