Solve 3x^2+x+2m-3=0

$$3 x ^ { 2 } + x + 2 m - 3 = 0$$

Solve for m

$$m=\frac{3-x-3x^{2}}{2}$$

Steps for Solving Linear Equation

Subtract 3x^{2} from both sides. Anything subtracted from zero gives its negation.

$$x+2m-3=-3x^{2}$$

Subtract x from both sides.

$$2m-3=-3x^{2}-x$$

Add 3 to both sides.

$$2m=-3x^{2}-x+3$$

The equation is in standard form.

$$2m=3-x-3x^{2}$$

Divide both sides by 2.

$$\frac{2m}{2}=\frac{3-x-3x^{2}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$m=\frac{3-x-3x^{2}}{2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{37-24m}-1}{6}$$

$$x=\frac{-\sqrt{37-24m}-1}{6}$$

Solve for x

$$x=\frac{\sqrt{37-24m}-1}{6}$$

$$x=\frac{-\sqrt{37-24m}-1}{6}\text{, }m\leq \frac{37}{24}$$