Solve 2ax^2+5x+6=0

$$2 a x ^ { 2 } + 5 x + 6 = 0$$

Solve for a

$$a=-\frac{5x+6}{2x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 5x from both sides. Anything subtracted from zero gives its negation.

$$2ax^{2}+6=-5x$$

Subtract 6 from both sides.

$$2ax^{2}=-5x-6$$

The equation is in standard form.

$$2x^{2}a=-5x-6$$

Divide both sides by 2x^{2}.

$$\frac{2x^{2}a}{2x^{2}}=\frac{-5x-6}{2x^{2}}$$

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

$$a=\frac{-5x-6}{2x^{2}}$$

Divide -5x-6 by 2x^{2}.

$$a=-\frac{\frac{5x}{2}+3}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{25-48a}-5}{4a}\text{; }x=-\frac{\sqrt{25-48a}+5}{4a}\text{, }&a\neq 0\\x=-\frac{6}{5}\text{, }&a=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{25-48a}-5}{4a}\text{; }x=-\frac{\sqrt{25-48a}+5}{4a}\text{, }&a\neq 0\text{ and }a\leq \frac{25}{48}\\x=-\frac{6}{5}\text{, }&a=0\end{matrix}\right.$$