x^2/(2x+3^2)-3x/2x=3+2=0

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To solve the equation: x^2/(2x+3)^2 - 3x/2x = 3 + 2 = 0, we first simplify the expression on the left side:

x^2/(2x+3)^2 - 3x/2x
= x^2/(2x+3)^2 - 3
= x^2/(2x+3)^2 - 3(2x)/(2x)
= x^2/(2x+3)^2 - 6x/(2x)
= x^2/(2x+3)^2 - 3

Now set this expression equal to 0:

x^2/(2x+3)^2 - 3 = 0

To solve this equation, we need to find a common denominator:

(x^2 - 3(2x)(2x+3)^2) / (2x+3)^2 = 0
(x^2 - 12x(2x+3) + 3) / (2x+3)^2 = 0

Expand and simplify the numerator:

x^2 - 12x(2x+3) + 3 = 0
x^2 - 24x^2 - 36x + 3 = 0
-23x^2 - 36x + 3 = 0

Now, we have a quadratic equation. We can use the quadratic formula to solve for x:

x = [-(-36) ± sqrt((-36)^2 - 4(-23)(3))]/(2(-23))
x = [36 ± sqrt(1296 + 276)]/(-46)
x = [36 ± sqrt(1572)]/(-46)
x = [36 ± 39.66]/(-46)
x = [75.66]/(-46) or x = [-3.66]/(-46)
x = -1.644, x = 0.08

Therefore, the solutions to the equation are x = -1.644 and x = 0.08.