M(x)=15x^2-2x-45

Solution for M(x)=15x^2-2x-45 equation:

(M)=15M^2-2M-45

We move all terms to the left:

(M)-(15M^2-2M-45)=0

We get rid of parentheses

-15M^2+M+2M+45=0

We add all the numbers together, and all the variables

-15M^2+3M+45=0

a = -15; b = 3; c = +45;
Δ = b2-4ac
Δ = 32-4·(-15)·45
Δ = 2709
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:

$\sqrt{\Delta}=\sqrt{2709}=\sqrt{9*301}=\sqrt{9}*\sqrt{301}=3\sqrt{301}$
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{301}}{2*-15}=\frac{-3-3\sqrt{301}}{-30}
$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{301}}{2*-15}=\frac{-3+3\sqrt{301}}{-30}
$