Solve -y=-6.8(x-50)^3+15

$$- y = - 6.8 ( x - 50 ) ^ { 3 } + 15$$

Solve for y

$$y=\frac{34\left(x-50\right)^{3}}{5}-15$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-50\right)^{3}.

$$-y=-6.8\left(x^{3}-150x^{2}+7500x-125000\right)+15$$

Use the distributive property to multiply -6.8 by x^{3}-150x^{2}+7500x-125000.

$$-y=-6.8x^{3}+1020x^{2}-51000x+850000+15$$

Add 850000 and 15 to get 850015.

$$-y=-6.8x^{3}+1020x^{2}-51000x+850015$$

The equation is in standard form.

$$-y=-\frac{34x^{3}}{5}+1020x^{2}-51000x+850015$$

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{-\frac{34x^{3}}{5}+1020x^{2}-51000x+850015}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{-\frac{34x^{3}}{5}+1020x^{2}-51000x+850015}{-1}$$

Divide -\frac{34x^{3}}{5}+1020x^{2}-51000x+850015 by -1.

$$y=\frac{34x^{3}}{5}-1020x^{2}+51000x-850015$$

Solve for x (complex solution)

$$x=\sqrt[3]{\frac{5y+75}{34}}+50$$

$$x=e^{\frac{i\times 4\pi }{3}}\sqrt[3]{\frac{5y+75}{34}}+50$$

$$x=e^{\frac{i\times 2\pi }{3}}\sqrt[3]{\frac{5y+75}{34}}+50$$

Solve for x

$$x=\sqrt[3]{\frac{5y+75}{34}}+50$$