M(x)=-x2+14x

Solution for M(x)=-x2+14x equation:

(M)=-M2+14M

We move all terms to the left:

(M)-(-M2+14M)=0

We add all the numbers together, and all the variables

-(-1M^2+14M)+M=0

We get rid of parentheses

1M^2-14M+M=0

We add all the numbers together, and all the variables

M^2-13M=0

a = 1; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·1·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*1}=\frac{0}{2}
=0
$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*1}=\frac{26}{2}
=13
$