M(x)=x2+106x-6000

Solution for M(x)=x2+106x-6000 equation:

(M)=M2+106M-6000

We move all terms to the left:

(M)-(M2+106M-6000)=0

We add all the numbers together, and all the variables

-(+M^2+106M-6000)+M=0

We get rid of parentheses

-M^2-106M+M+6000=0

We add all the numbers together, and all the variables

-1M^2-105M+6000=0

a = -1; b = -105; c = +6000;
Δ = b2-4ac
Δ = -1052-4·(-1)·6000
Δ = 35025
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:

$\sqrt{\Delta}=\sqrt{35025}=\sqrt{25*1401}=\sqrt{25}*\sqrt{1401}=5\sqrt{1401}$
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-5\sqrt{1401}}{2*-1}=\frac{105-5\sqrt{1401}}{-2}
$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+5\sqrt{1401}}{2*-1}=\frac{105+5\sqrt{1401}}{-2}
$