4(9-m)m=4

Solution for 4(9-m)m=4 equation:

4(9-m)m=4

We move all terms to the left:

4(9-m)m-(4)=0

We add all the numbers together, and all the variables

4(-1m+9)m-4=0

We multiply parentheses

-4m^2+36m-4=0

a = -4; b = 36; c = -4;
Δ = b2-4ac
Δ = 362-4·(-4)·(-4)
Δ = 1232
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:

$\sqrt{\Delta}=\sqrt{1232}=\sqrt{16*77}=\sqrt{16}*\sqrt{77}=4\sqrt{77}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{77}}{2*-4}=\frac{-36-4\sqrt{77}}{-8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{77}}{2*-4}=\frac{-36+4\sqrt{77}}{-8}
$