3/4m=7-m

Solution for 3/4m=7-m equation:

3/4m=7-m

We move all terms to the left:

3/4m-(7-m)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R


We add all the numbers together, and all the variables

3/4m-(-1m+7)=0

We get rid of parentheses

3/4m+1m-7=0

We multiply all the terms by the denominator


1m*4m-7*4m+3=0

Wy multiply elements

4m^2-28m+3=0

a = 4; b = -28; c = +3;
Δ = b2-4ac
Δ = -282-4·4·3
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{46}}{2*4}=\frac{28-4\sqrt{46}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{46}}{2*4}=\frac{28+4\sqrt{46}}{8}
$