-3/4*m=-6

Solution for -3/4*m=-6 equation:

-3/4*m=-6

We move all terms to the left:

-3/4*m-(-6)=0


Domain of the equation: 4*m!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

-3/4*m+6=0

We multiply all the terms by the denominator


6*4*m-3=0

Wy multiply elements

24m*m-3=0

Wy multiply elements

24m^2-3=0

a = 24; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·24·(-3)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*24}=\frac{0-12\sqrt{2}}{48}
=-\frac{12\sqrt{2}}{48}
=-\frac{\sqrt{2}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*24}=\frac{0+12\sqrt{2}}{48}
=\frac{12\sqrt{2}}{48}
=\frac{\sqrt{2}}{4}
$