A(x)=150x+2x^2

Solution for A(x)=150x+2x^2 equation:

(A)=150A+2A^2

We move all terms to the left:

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

We get rid of parentheses

-2A^2-150A+A=0

We add all the numbers together, and all the variables

-2A^2-149A=0

a = -2; b = -149; c = 0;
Δ = b2-4ac
Δ = -1492-4·(-2)·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*-2}=\frac{0}{-4}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-149)+149}{2*-2}=\frac{298}{-4}
=-74+1/2
$