M(x)=2x^2-7x+3

Solution for M(x)=2x^2-7x+3 equation:

(M)=2M^2-7M+3

We move all terms to the left:

(M)-(2M^2-7M+3)=0

We get rid of parentheses

-2M^2+M+7M-3=0

We add all the numbers together, and all the variables

-2M^2+8M-3=0

a = -2; b = 8; c = -3;
Δ = b2-4ac
Δ = 82-4·(-2)·(-3)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{10}}{2*-2}=\frac{-8-2\sqrt{10}}{-4}
$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{10}}{2*-2}=\frac{-8+2\sqrt{10}}{-4}
$