3a^2+b^2=7a^2

Solution for 3a^2+b^2=7a^2 equation:

Simplifying
3a2 + b2 = 7a2

Solving
3a2 + b2 = 7a2

Solving for variable 'a'.

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

Add '-7a2' to each side of the equation.
3a2 + -7a2 + b2 = 7a2 + -7a2

Combine like terms: 3a2 + -7a2 = -4a2
-4a2 + b2 = 7a2 + -7a2

Combine like terms: 7a2 + -7a2 = 0
-4a2 + b2 = 0

Add '-1b2' to each side of the equation.
-4a2 + b2 + -1b2 = 0 + -1b2

Combine like terms: b2 + -1b2 = 0
-4a2 + 0 = 0 + -1b2
-4a2 = 0 + -1b2
Remove the zero:
-4a2 = -1b2

Divide each side by '-4'.
a2 = 0.25b2

Simplifying
a2 = 0.25b2

Take the square root of each side:
a = {-0.5b, 0.5b}