A=x(2x+3)

Solution for A=x(2x+3) equation:

=A(2A+3)

We move all terms to the left:

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


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

A(2A+3)

We multiply parentheses

2A^2+3A

Back to the equation:

-(2A^2+3A)


We get rid of parentheses

-2A^2-3A=0

a = -2; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-2)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-2}=\frac{0}{-4}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-2}=\frac{6}{-4}
=-1+1/2
$