3/4m+m=5

Solution for 3/4m+m=5 equation:

3/4m+m=5

We move all terms to the left:

3/4m+m-(5)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R


We add all the numbers together, and all the variables

m+3/4m-5=0

We multiply all the terms by the denominator


m*4m-5*4m+3=0

Wy multiply elements

4m^2-20m+3=0

a = 4; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·4·3
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{22}}{2*4}=\frac{20-4\sqrt{22}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{22}}{2*4}=\frac{20+4\sqrt{22}}{8}
$