m21/2c-c=12

Solution for m21/2c-c=12 equation:

21/2M-M=12

We move all terms to the left:

21/2M-M-(12)=0


Domain of the equation: 2M!=0

M!=0/2

M!=0

M∈R


We add all the numbers together, and all the variables

-1M+21/2M-12=0

We multiply all the terms by the denominator


-1M*2M-12*2M+21=0

Wy multiply elements

-2M^2-24M+21=0

a = -2; b = -24; c = +21;
Δ = b2-4ac
Δ = -242-4·(-2)·21
Δ = 744
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:

$\sqrt{\Delta}=\sqrt{744}=\sqrt{4*186}=\sqrt{4}*\sqrt{186}=2\sqrt{186}$
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{186}}{2*-2}=\frac{24-2\sqrt{186}}{-4}
$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{186}}{2*-2}=\frac{24+2\sqrt{186}}{-4}
$