(1/2)m-(3/4)(8)=16

Solution for (1/2)m-(3/4)(8)=16 equation:

(1/2)m-(3/4)(8)=16

We move all terms to the left:

(1/2)m-(3/4)(8)-(16)=0


Domain of the equation: 2)m!=0

m!=0/1

m!=0

m∈R


determiningTheFunctionDomain
(1/2)m-16-(3/4)8=0

We add all the numbers together, and all the variables

(+1/2)m-16-(+3/4)8=0

We multiply parentheses

m^2-16-3/4*8=0

We multiply all the terms by the denominator


m^2*4*8-3-16*4*8=0

We add all the numbers together, and all the variables

m^2*4*8-515=0

Wy multiply elements

32m^2*8-515=0

Wy multiply elements

256m^2-515=0

a = 256; b = 0; c = -515;
Δ = b2-4ac
Δ = 02-4·256·(-515)
Δ = 527360
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:

$\sqrt{\Delta}=\sqrt{527360}=\sqrt{1024*515}=\sqrt{1024}*\sqrt{515}=32\sqrt{515}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{515}}{2*256}=\frac{0-32\sqrt{515}}{512}
=-\frac{32\sqrt{515}}{512}
=-\frac{\sqrt{515}}{16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{515}}{2*256}=\frac{0+32\sqrt{515}}{512}
=\frac{32\sqrt{515}}{512}
=\frac{\sqrt{515}}{16}
$