Solve DeltaK=1/2mx^frac{2{1}+1}1/2nv^frac{2{2}}

$$\Delta K = \frac { 1 } { 2 } m x ^ { \frac { 2 } { 1 } + 1 } \frac { 1 } { 2 } n v ^ { \frac { 2 } { 2 } }$$

Solve for K (complex solution)

$$\left\{\begin{matrix}K=\frac{mnvx^{3}}{4\Delta }\text{, }&\Delta \neq 0\\K\in \mathrm{C}\text{, }&\left(x=0\text{ or }m=0\text{ or }n=0\text{ or }v=0\right)\text{ and }\Delta =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Anything divided by one gives itself.

$$\Delta K=\frac{1}{2}mx^{2+1}\times \frac{1}{2}nv^{\frac{2}{2}}$$

Add 2 and 1 to get 3.

$$\Delta K=\frac{1}{2}mx^{3}\times \frac{1}{2}nv^{\frac{2}{2}}$$

Multiply \frac{1}{2} and \frac{1}{2} to get \frac{1}{4}.

$$\Delta K=\frac{1}{4}mx^{3}nv^{\frac{2}{2}}$$

Divide 2 by 2 to get 1.

$$\Delta K=\frac{1}{4}mx^{3}nv^{1}$$

Calculate v to the power of 1 and get v.

$$\Delta K=\frac{1}{4}mx^{3}nv$$

The equation is in standard form.

$$\Delta K=\frac{mnvx^{3}}{4}$$

Divide both sides by \Delta .

$$\frac{\Delta K}{\Delta }=\frac{mnvx^{3}}{4\Delta }$$

Dividing by \Delta undoes the multiplication by \Delta .

$$K=\frac{mnvx^{3}}{4\Delta }$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{4K\Delta }{nvx^{3}}\text{, }&v\neq 0\text{ and }n\neq 0\text{ and }x\neq 0\\m\in \mathrm{C}\text{, }&\left(\Delta =0\text{ and }x=0\right)\text{ or }\left(n=0\text{ and }\Delta =0\right)\text{ or }\left(v=0\text{ and }\Delta =0\right)\text{ or }\left(K=0\text{ and }x=0\right)\text{ or }\left(K=0\text{ and }n=0\right)\text{ or }\left(K=0\text{ and }v=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Anything divided by one gives itself.

$$\Delta K=\frac{1}{2}mx^{2+1}\times \frac{1}{2}nv^{\frac{2}{2}}$$

Add 2 and 1 to get 3.

$$\Delta K=\frac{1}{2}mx^{3}\times \frac{1}{2}nv^{\frac{2}{2}}$$

Multiply \frac{1}{2} and \frac{1}{2} to get \frac{1}{4}.

$$\Delta K=\frac{1}{4}mx^{3}nv^{\frac{2}{2}}$$

Divide 2 by 2 to get 1.

$$\Delta K=\frac{1}{4}mx^{3}nv^{1}$$

Calculate v to the power of 1 and get v.

$$\Delta K=\frac{1}{4}mx^{3}nv$$

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

$$\frac{1}{4}mx^{3}nv=\Delta K$$

The equation is in standard form.

$$\frac{nvx^{3}}{4}m=K\Delta$$

Divide both sides by \frac{1}{4}x^{3}nv.

$$\frac{4\times \frac{nvx^{3}}{4}m}{nvx^{3}}=\frac{4K\Delta }{nvx^{3}}$$

Dividing by \frac{1}{4}x^{3}nv undoes the multiplication by \frac{1}{4}x^{3}nv.

$$m=\frac{4K\Delta }{nvx^{3}}$$

Solve for K

$$\left\{\begin{matrix}K=\frac{mnvx^{3}}{4\Delta }\text{, }&\Delta \neq 0\\K\in \mathrm{R}\text{, }&\left(x=0\text{ or }m=0\text{ or }n=0\text{ or }v=0\right)\text{ and }\Delta =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Anything divided by one gives itself.

$$\Delta K=\frac{1}{2}mx^{2+1}\times \frac{1}{2}nv^{\frac{2}{2}}$$

Add 2 and 1 to get 3.

$$\Delta K=\frac{1}{2}mx^{3}\times \frac{1}{2}nv^{\frac{2}{2}}$$

Multiply \frac{1}{2} and \frac{1}{2} to get \frac{1}{4}.

$$\Delta K=\frac{1}{4}mx^{3}nv^{\frac{2}{2}}$$

Divide 2 by 2 to get 1.

$$\Delta K=\frac{1}{4}mx^{3}nv^{1}$$

Calculate v to the power of 1 and get v.

$$\Delta K=\frac{1}{4}mx^{3}nv$$

The equation is in standard form.

$$\Delta K=\frac{mnvx^{3}}{4}$$

Divide both sides by \Delta .

$$\frac{\Delta K}{\Delta }=\frac{mnvx^{3}}{4\Delta }$$

Dividing by \Delta undoes the multiplication by \Delta .

$$K=\frac{mnvx^{3}}{4\Delta }$$

Solve for m

$$\left\{\begin{matrix}m=\frac{4K\Delta }{nvx^{3}}\text{, }&v\neq 0\text{ and }n\neq 0\text{ and }x\neq 0\\m\in \mathrm{R}\text{, }&\left(\Delta =0\text{ and }x=0\right)\text{ or }\left(n=0\text{ and }\Delta =0\right)\text{ or }\left(v=0\text{ and }\Delta =0\right)\text{ or }\left(K=0\text{ and }x=0\right)\text{ or }\left(K=0\text{ and }n=0\right)\text{ or }\left(K=0\text{ and }v=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Anything divided by one gives itself.

$$\Delta K=\frac{1}{2}mx^{2+1}\times \frac{1}{2}nv^{\frac{2}{2}}$$

Add 2 and 1 to get 3.

$$\Delta K=\frac{1}{2}mx^{3}\times \frac{1}{2}nv^{\frac{2}{2}}$$

Multiply \frac{1}{2} and \frac{1}{2} to get \frac{1}{4}.

$$\Delta K=\frac{1}{4}mx^{3}nv^{\frac{2}{2}}$$

Divide 2 by 2 to get 1.

$$\Delta K=\frac{1}{4}mx^{3}nv^{1}$$

Calculate v to the power of 1 and get v.

$$\Delta K=\frac{1}{4}mx^{3}nv$$

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

$$\frac{1}{4}mx^{3}nv=\Delta K$$

The equation is in standard form.

$$\frac{nvx^{3}}{4}m=K\Delta$$

Divide both sides by \frac{1}{4}x^{3}nv.

$$\frac{4\times \frac{nvx^{3}}{4}m}{nvx^{3}}=\frac{4K\Delta }{nvx^{3}}$$

Dividing by \frac{1}{4}x^{3}nv undoes the multiplication by \frac{1}{4}x^{3}nv.

$$m=\frac{4K\Delta }{nvx^{3}}$$