Solve -y=-9/5(x-40)^3+30

$$- y = - \frac { 9 } { 5 } ( x - 40 ) ^ { 3 } + 30$$

Solve for y

$$y=\frac{9\left(x-40\right)^{3}}{5}-30$$

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-40\right)^{3}.

$$-y=-\frac{9}{5}\left(x^{3}-120x^{2}+4800x-64000\right)+30$$

Use the distributive property to multiply -\frac{9}{5} by x^{3}-120x^{2}+4800x-64000.

$$-y=-\frac{9}{5}x^{3}+216x^{2}-8640x+115200+30$$

Add 115200 and 30 to get 115230.

$$-y=-\frac{9}{5}x^{3}+216x^{2}-8640x+115230$$

The equation is in standard form.

$$-y=-\frac{9x^{3}}{5}+216x^{2}-8640x+115230$$

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{-\frac{9x^{3}}{5}+216x^{2}-8640x+115230}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{-\frac{9x^{3}}{5}+216x^{2}-8640x+115230}{-1}$$

Divide -\frac{9x^{3}}{5}+216x^{2}-8640x+115230 by -1.

$$y=\frac{9x^{3}}{5}-216x^{2}+8640x-115230$$

Solve for x

$$x=\frac{\sqrt[3]{15\left(y+30\right)}+120}{3}$$