Solve nu = 1/2 + (epsilon)/(6*(4*pi)^2) phi^4

Evaluate

ν = \frac{1}{2} + \frac{ϵ}{6 ( 4 π ) ^{2}} \times ϕ^{4}

Simplify

More Steps

ν = \frac{1}{2} + \frac{ϵ ϕ ^{4}}{96 π ^{2}}

Evaluate

ν = \frac{1}{2} + \frac{ϵ}{6 ( 4 π ) ^{2}} \times ϕ^{4}

Simplify

More Steps

ν = \frac{1}{2} + \frac{ϵ ϕ ^{4}}{96 π ^{2}}

Rewrite the expression

ν = \frac{1}{2} + \frac{ϕ ^{4} ϵ}{96 π ^{2}}

Swap the sides of the equation

\frac{1}{2} + \frac{ϕ ^{4} ϵ}{96 π ^{2}} = ν

Move the constant to the right-hand side and change its sign

\frac{ϕ ^{4} ϵ}{96 π ^{2}} = ν - \frac{1}{2}

Subtract the terms

More Steps

\frac{ϕ ^{4} ϵ}{96 π ^{2}} = \frac{2 ν - 1}{2}

Multiply both sides of the equation by 96 π^{2}

\frac{ϕ ^{4} ϵ}{96 π ^{2}} \times 96 π^{2} = \frac{2 ν - 1}{2} \times 96 π^{2}

Multiply the terms

ϕ^{4} ϵ = \frac{( 2 ν - 1 ) \times 96 π ^{2}}{2}

Divide the terms

ϕ^{4} ϵ = 96 ν π^{2} - 48 π^{2}

Divide both sides

\frac{ϕ ^{4} ϵ}{ϕ ^{4}} = \frac{96 ν π ^{2} - 48 π ^{2}}{ϕ ^{4}}

Divide the numbers

ϵ = \frac{96 ν π ^{2} - 48 π ^{2}}{ϕ ^{4}}

Solution

ϵ = \frac{96 π ^{2} ν - 48 π ^{2}}{ϕ ^{4}}

Function