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

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

Solve for y

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

Solution Steps

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 -115170.

$$y=\frac{9}{5}x^{3}-216x^{2}+8640x-115170$$

Solve for x

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