4y^2-2.5=y^2+4.25

Solution for 4y^2-2.5=y^2+4.25 equation:

Simplifying
4y2 + -2.5 = y2 + 4.25

Reorder the terms:
-2.5 + 4y2 = y2 + 4.25

Reorder the terms:
-2.5 + 4y2 = 4.25 + y2

Solving
-2.5 + 4y2 = 4.25 + y2

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-1y2' to each side of the equation.
-2.5 + 4y2 + -1y2 = 4.25 + y2 + -1y2

Combine like terms: 4y2 + -1y2 = 3y2
-2.5 + 3y2 = 4.25 + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-2.5 + 3y2 = 4.25 + 0
-2.5 + 3y2 = 4.25

Add '2.5' to each side of the equation.
-2.5 + 2.5 + 3y2 = 4.25 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 3y2 = 4.25 + 2.5
3y2 = 4.25 + 2.5

Combine like terms: 4.25 + 2.5 = 6.75
3y2 = 6.75

Divide each side by '3'.
y2 = 2.25

Simplifying
y2 = 2.25

Take the square root of each side:
y = {-1.5, 1.5}