Solve 2u^2/1=x+2/3

$$\frac { 2 u ^ { 2 } } { 1 } = \frac { x + 2 } { 3 }$$

Solve for x

$$x=6u^{2}-2$$

Solution Steps

Multiply both sides of the equation by 3.

$$3\times 2u^{2}=x+2$$

Multiply 3 and 2 to get 6.

$$6u^{2}=x+2$$

Swap sides so that all variable terms are on the left hand side.

$$x+2=6u^{2}$$

Subtract 2 from both sides.

$$x=6u^{2}-2$$

Solve for u (complex solution)

$$u=-\frac{\sqrt{6\left(x+2\right)}}{6}$$

$$u=\frac{\sqrt{6\left(x+2\right)}}{6}$$

Solve for u

$$u=\frac{\sqrt{6\left(x+2\right)}}{6}$$

$$u=-\frac{\sqrt{6\left(x+2\right)}}{6}\text{, }x\geq -2$$