Solve (20x)^2+5xm-(60x)^2/40x*20sqrt{13}=frac{5sqrt{3}}{26}

$$\frac { ( 20 x ) ^ { 2 } + 5 x m - ( 60 x ) ^ { 2 } } { 40 x \times 20 \sqrt { 13 } } = \frac { 5 \sqrt { 3 } } { 26 }$$

Solve for m

$$m=640x+\frac{400\sqrt{39}}{13}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 26.

$$\frac{1}{400}x^{-1}\times 13^{\frac{1}{2}}\left(\left(20x\right)^{2}+5xm-\left(60x\right)^{2}\right)=5\sqrt{3}$$

Expand \left(20x\right)^{2}.

$$\frac{1}{400}x^{-1}\times 13^{\frac{1}{2}}\left(20^{2}x^{2}+5xm-\left(60x\right)^{2}\right)=5\sqrt{3}$$

Calculate 20 to the power of 2 and get 400.

$$\frac{1}{400}x^{-1}\times 13^{\frac{1}{2}}\left(400x^{2}+5xm-\left(60x\right)^{2}\right)=5\sqrt{3}$$

Expand \left(60x\right)^{2}.

$$\frac{1}{400}x^{-1}\times 13^{\frac{1}{2}}\left(400x^{2}+5xm-60^{2}x^{2}\right)=5\sqrt{3}$$

Calculate 60 to the power of 2 and get 3600.

$$\frac{1}{400}x^{-1}\times 13^{\frac{1}{2}}\left(400x^{2}+5xm-3600x^{2}\right)=5\sqrt{3}$$

Combine 400x^{2} and -3600x^{2} to get -3200x^{2}.

$$\frac{1}{400}x^{-1}\times 13^{\frac{1}{2}}\left(-3200x^{2}+5xm\right)=5\sqrt{3}$$

Use the distributive property to multiply \frac{1}{400}x^{-1}\times 13^{\frac{1}{2}} by -3200x^{2}+5xm.

$$-8x\times 13^{\frac{1}{2}}+\frac{1}{80}m\times 13^{\frac{1}{2}}=5\sqrt{3}$$

Add 8x\times 13^{\frac{1}{2}} to both sides.

$$\frac{1}{80}m\times 13^{\frac{1}{2}}=5\sqrt{3}+8x\times 13^{\frac{1}{2}}$$

Reorder the terms.

$$\frac{1}{80}\sqrt{13}m=8\sqrt{13}x+5\sqrt{3}$$

The equation is in standard form.

$$\frac{\sqrt{13}}{80}m=8\sqrt{13}x+5\sqrt{3}$$

Divide both sides by \frac{1}{80}\sqrt{13}.

$$\frac{80\times \frac{\sqrt{13}}{80}m}{\sqrt{13}}=\frac{80\left(8\sqrt{13}x+5\sqrt{3}\right)}{\sqrt{13}}$$

Dividing by \frac{1}{80}\sqrt{13} undoes the multiplication by \frac{1}{80}\sqrt{13}.

$$m=\frac{80\left(8\sqrt{13}x+5\sqrt{3}\right)}{\sqrt{13}}$$

Divide 8\sqrt{13}x+5\sqrt{3} by \frac{1}{80}\sqrt{13}.

$$m=640x+\frac{400\sqrt{39}}{13}$$

Solve for x

$$x=\frac{m}{640}-\frac{5\sqrt{39}}{104}$$

$$m\neq \frac{400\sqrt{39}}{13}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 26.

$$\frac{1}{400}x^{-1}\times 13^{\frac{1}{2}}\left(\left(20x\right)^{2}+5xm-\left(60x\right)^{2}\right)=5\sqrt{3}$$

Expand \left(20x\right)^{2}.

$$\frac{1}{400}x^{-1}\times 13^{\frac{1}{2}}\left(20^{2}x^{2}+5xm-\left(60x\right)^{2}\right)=5\sqrt{3}$$

Calculate 20 to the power of 2 and get 400.

$$\frac{1}{400}x^{-1}\times 13^{\frac{1}{2}}\left(400x^{2}+5xm-\left(60x\right)^{2}\right)=5\sqrt{3}$$

Expand \left(60x\right)^{2}.

$$\frac{1}{400}x^{-1}\times 13^{\frac{1}{2}}\left(400x^{2}+5xm-60^{2}x^{2}\right)=5\sqrt{3}$$

Calculate 60 to the power of 2 and get 3600.

$$\frac{1}{400}x^{-1}\times 13^{\frac{1}{2}}\left(400x^{2}+5xm-3600x^{2}\right)=5\sqrt{3}$$

Combine 400x^{2} and -3600x^{2} to get -3200x^{2}.

$$\frac{1}{400}x^{-1}\times 13^{\frac{1}{2}}\left(-3200x^{2}+5xm\right)=5\sqrt{3}$$

Use the distributive property to multiply \frac{1}{400}x^{-1}\times 13^{\frac{1}{2}} by -3200x^{2}+5xm.

$$-8x\times 13^{\frac{1}{2}}+\frac{1}{80}\times 13^{\frac{1}{2}}m=5\sqrt{3}$$

Subtract \frac{1}{80}\times 13^{\frac{1}{2}}m from both sides.

$$-8x\times 13^{\frac{1}{2}}=5\sqrt{3}-\frac{1}{80}\times 13^{\frac{1}{2}}m$$

Reorder the terms.

$$-8\sqrt{13}x=5\sqrt{3}-\frac{1}{80}\sqrt{13}m$$

The equation is in standard form.

$$\left(-8\sqrt{13}\right)x=-\frac{\sqrt{13}m}{80}+5\sqrt{3}$$

Divide both sides by -8\sqrt{13}.

$$\frac{\left(-8\sqrt{13}\right)x}{-8\sqrt{13}}=\frac{-\frac{\sqrt{13}m}{80}+5\sqrt{3}}{-8\sqrt{13}}$$

Dividing by -8\sqrt{13} undoes the multiplication by -8\sqrt{13}.

$$x=\frac{-\frac{\sqrt{13}m}{80}+5\sqrt{3}}{-8\sqrt{13}}$$

Divide 5\sqrt{3}-\frac{\sqrt{13}m}{80} by -8\sqrt{13}.

$$x=\frac{m}{640}-\frac{5\sqrt{39}}{104}$$