Solve quadtext{(g)}60x^2+57x=18

$$\quad \text { (g) } 60 x ^ { 2 } + 57 x = 18$$

Solve for g

$$g=-\frac{19x-6}{20x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 57x from both sides.

$$g\times 60x^{2}=18-57x$$

The equation is in standard form.

$$60x^{2}g=18-57x$$

Divide both sides by 60x^{2}.

$$\frac{60x^{2}g}{60x^{2}}=\frac{18-57x}{60x^{2}}$$

Dividing by 60x^{2} undoes the multiplication by 60x^{2}.

$$g=\frac{18-57x}{60x^{2}}$$

Divide 18-57x by 60x^{2}.

$$g=\frac{6-19x}{20x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{480g+361}-19}{40g}\text{; }x=-\frac{\sqrt{480g+361}+19}{40g}\text{, }&g\neq 0\\x=\frac{6}{19}\text{, }&g=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{480g+361}-19}{40g}\text{; }x=-\frac{\sqrt{480g+361}+19}{40g}\text{, }&g\neq 0\text{ and }g\geq -\frac{361}{480}\\x=\frac{6}{19}\text{, }&g=0\end{matrix}\right.$$