Solve 76/a=left(1.5-hright)^3+k

$$\frac{ 76 }{ a } = { \left(1.5-h \right) }^{ 3 } +k$$

Solve for a

$$a=\frac{608}{27+8k-54h+36h^{2}-8h^{3}}$$

$$h\neq \sqrt[3]{\frac{|k|+k}{2}}+\sqrt[3]{\frac{k-|k|}{2}}+\frac{3}{2}$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$76=a\left(1.5-h\right)^{3}+ak$$

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(1.5-h\right)^{3}.

$$76=a\left(3.375-6.75h+4.5h^{2}-h^{3}\right)+ak$$

Use the distributive property to multiply a by 3.375-6.75h+4.5h^{2}-h^{3}.

$$76=3.375a-6.75ah+4.5ah^{2}-ah^{3}+ak$$

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

$$3.375a-6.75ah+4.5ah^{2}-ah^{3}+ak=76$$

Combine all terms containing a.

$$\left(3.375-6.75h+4.5h^{2}-h^{3}+k\right)a=76$$

The equation is in standard form.

$$\left(-h^{3}+\frac{9h^{2}}{2}-\frac{27h}{4}+k+3.375\right)a=76$$

Divide both sides by 3.375-6.75h+4.5h^{2}-h^{3}+k.

$$\frac{\left(-h^{3}+\frac{9h^{2}}{2}-\frac{27h}{4}+k+3.375\right)a}{-h^{3}+\frac{9h^{2}}{2}-\frac{27h}{4}+k+3.375}=\frac{76}{-h^{3}+\frac{9h^{2}}{2}-\frac{27h}{4}+k+3.375}$$

Dividing by 3.375-6.75h+4.5h^{2}-h^{3}+k undoes the multiplication by 3.375-6.75h+4.5h^{2}-h^{3}+k.

$$a=\frac{76}{-h^{3}+\frac{9h^{2}}{2}-\frac{27h}{4}+k+3.375}$$

Divide 76 by 3.375-6.75h+4.5h^{2}-h^{3}+k.

$$a=\frac{608}{27+8k-54h+36h^{2}-8h^{3}}$$

Variable a cannot be equal to 0.

$$a=\frac{608}{27+8k-54h+36h^{2}-8h^{3}}\text{, }a\neq 0$$

Solve for h

$$h=-\sqrt[3]{-k+\frac{76}{a}}+1.5$$

$$a\neq 0$$