Distribute the 5 on the left side of the equation: 45 - 5x^2 = x^2 - 3x

Rearrange the equation: 5x^2 + x^2 - 3x + 45 = 0

Combine like terms: 6x^2 - 3x + 45 = 0

Distribute x on the left side of the equation: 2x^2 + x = 4x + 1

Rearrange the equation: 2x^2 - 3x - 1 = 0

Distribute x on the left side of the equation: 2x^2 + 2x = x^2 - 1

Rearrange the equation: x^2 + 2x + 1 = 0

Factor the equation: (x + 1)^2 = 0

Therefore, the solutions for the equations are:
6x^2 - 3x + 45 = 0
2x^2 - 3x - 1 = 0
(x + 1)^2 = 0

x = -1/2 ± √(221)/6, x = 1/2 ± √(3)/2
x = (x = 1)