11+m=-7/4m

Solution for 11+m=-7/4m equation:

11+m=-7/4m

We move all terms to the left:

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


Domain of the equation: 4m)!=0

m!=0/1

m!=0

m∈R


We get rid of parentheses

m+7/4m+11=0

We multiply all the terms by the denominator


m*4m+11*4m+7=0

Wy multiply elements

4m^2+44m+7=0

a = 4; b = 44; c = +7;
Δ = b2-4ac
Δ = 442-4·4·7
Δ = 1824
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:

$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{114}}{2*4}=\frac{-44-4\sqrt{114}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{114}}{2*4}=\frac{-44+4\sqrt{114}}{8}
$