A(x)=-x2+150x

Solution for A(x)=-x2+150x equation:

(A)=-A2+150A

We move all terms to the left:

(A)-(-A2+150A)=0

We add all the numbers together, and all the variables

-(-1A^2+150A)+A=0

We get rid of parentheses

1A^2-150A+A=0

We add all the numbers together, and all the variables

A^2-149A=0

a = 1; b = -149; c = 0;
Δ = b2-4ac
Δ = -1492-4·1·0
Δ = 22201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22201}=149$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-149)-149}{2*1}=\frac{0}{2}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-149)+149}{2*1}=\frac{298}{2}
=149
$