M(x)=3X2-5x-3

Solution for M(x)=3X2-5x-3 equation:

(M)=3M^2-5M-3

We move all terms to the left:

(M)-(3M^2-5M-3)=0

We get rid of parentheses

-3M^2+M+5M+3=0

We add all the numbers together, and all the variables

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

a = -3; b = 6; c = +3;
Δ = b2-4ac
Δ = 62-4·(-3)·3
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{2}}{2*-3}=\frac{-6-6\sqrt{2}}{-6}
$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{2}}{2*-3}=\frac{-6+6\sqrt{2}}{-6}
$