A=x(60-1.5x)

Solution for A=x(60-1.5x) equation:

=A(60-1.5A)

We move all terms to the left:

-(A(60-1.5A))=0

We add all the numbers together, and all the variables

-(A(-1.5A+60))=0


We calculate terms in parentheses: -(A(-1.5A+60)), so:

A(-1.5A+60)

We multiply parentheses

-1A^2+60A

Back to the equation:

-(-1A^2+60A)


We get rid of parentheses

1A^2-60A=0

We add all the numbers together, and all the variables

A^2-60A=0

a = 1; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·1·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*1}=\frac{0}{2}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*1}=\frac{120}{2}
=60
$