7/4m+m=22

Solution for 7/4m+m=22 equation:

7/4m+m=22

We move all terms to the left:

7/4m+m-(22)=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+7/4m-22=0

We multiply all the terms by the denominator


m*4m-22*4m+7=0

Wy multiply elements

4m^2-88m+7=0

a = 4; b = -88; c = +7;
Δ = b2-4ac
Δ = -882-4·4·7
Δ = 7632
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:

$\sqrt{\Delta}=\sqrt{7632}=\sqrt{144*53}=\sqrt{144}*\sqrt{53}=12\sqrt{53}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-12\sqrt{53}}{2*4}=\frac{88-12\sqrt{53}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+12\sqrt{53}}{2*4}=\frac{88+12\sqrt{53}}{8}
$