M=6q-3/q+2

Solution for M=6q-3/q+2 equation:

=6M-3/M+2

We move all terms to the left:

-(6M-3/M+2)=0


Domain of the equation: M+2)!=0

M∈R


We get rid of parentheses

-6M+3/M-2=0

We multiply all the terms by the denominator


-6M*M-2*M+3=0

We add all the numbers together, and all the variables

-2M-6M*M+3=0

Wy multiply elements

-6M^2-2M+3=0

a = -6; b = -2; c = +3;
Δ = b2-4ac
Δ = -22-4·(-6)·3
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{19}}{2*-6}=\frac{2-2\sqrt{19}}{-12}
$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{19}}{2*-6}=\frac{2+2\sqrt{19}}{-12}
$