Solve 60x-x^2=86varphi

$$60 x - x ^ { 2 } = 86 \varphi$$

Solve for φ

$$\phi =\frac{x\left(60-x\right)}{86}$$

Steps for Solving Linear Equation

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

$$86\phi =60x-x^{2}$$

Divide both sides by 86.

$$\frac{86\phi }{86}=\frac{x\left(60-x\right)}{86}$$

Dividing by 86 undoes the multiplication by 86.

$$\phi =\frac{x\left(60-x\right)}{86}$$

Solve for x (complex solution)

$$x=-\sqrt{900-86\phi }+30$$

$$x=\sqrt{900-86\phi }+30$$

Solve for x

$$x=-\sqrt{900-86\phi }+30$$

$$x=\sqrt{900-86\phi }+30\text{, }\phi \leq \frac{450}{43}$$