A=2x(8-3x)

Solution for A=2x(8-3x) equation:

=2A(8-3A)

We move all terms to the left:

-(2A(8-3A))=0

We add all the numbers together, and all the variables

-(2A(-3A+8))=0


We calculate terms in parentheses: -(2A(-3A+8)), so:

2A(-3A+8)

We multiply parentheses

-6A^2+16A

Back to the equation:

-(-6A^2+16A)


We get rid of parentheses

6A^2-16A=0

a = 6; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·6·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*6}=\frac{0}{12}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*6}=\frac{32}{12}
=2+2/3
$