A=a*(150-2*a)

Solution for A=a*(150-2*a) equation:

=A(150-2A)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(A(-2A+150)), so:

A(-2A+150)

We multiply parentheses

-2A^2+150A

Back to the equation:

-(-2A^2+150A)


We get rid of parentheses

2A^2-150A=0

a = 2; b = -150; c = 0;
Δ = b2-4ac
Δ = -1502-4·2·0
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-150}{2*2}=\frac{0}{4}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+150}{2*2}=\frac{300}{4}
=75
$