Solve 4x^2-20x-24g+97=0

$$4 x ^ { 2 } - 20 x - 24 g + 97 = 0$$

Solve for g

$$g=\frac{x^{2}}{6}-\frac{5x}{6}+\frac{97}{24}$$

Steps for Solving Linear Equation

Subtract 4x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-20x-24g+97=-4x^{2}$$

Add 20x to both sides.

$$-24g+97=-4x^{2}+20x$$

Subtract 97 from both sides.

$$-24g=-4x^{2}+20x-97$$

Divide both sides by -24.

$$\frac{-24g}{-24}=\frac{-4x^{2}+20x-97}{-24}$$

Dividing by -24 undoes the multiplication by -24.

$$g=\frac{-4x^{2}+20x-97}{-24}$$

Divide -4x^{2}+20x-97 by -24.

$$g=\frac{x^{2}}{6}-\frac{5x}{6}+\frac{97}{24}$$

Solve for x (complex solution)

$$x=\sqrt{6g-18}+\frac{5}{2}$$

$$x=-\sqrt{6g-18}+\frac{5}{2}$$

Solve for x

$$x=\sqrt{6g-18}+\frac{5}{2}$$

$$x=-\sqrt{6g-18}+\frac{5}{2}\text{, }g\geq 3$$