Solve lambda^2+75x-1900=0

$$\lambda ^ { 2 } + 75 x - 1900 = 0$$

Solve for x

$$x=-\frac{\lambda ^{2}}{75}+\frac{76}{3}$$

Steps for Solving Linear Equation

Subtract \lambda ^{2} from both sides. Anything subtracted from zero gives its negation.

$$75x-1900=-\lambda ^{2}$$

Add 1900 to both sides.

$$75x=-\lambda ^{2}+1900$$

The equation is in standard form.

$$75x=1900-\lambda ^{2}$$

Divide both sides by 75.

$$\frac{75x}{75}=\frac{1900-\lambda ^{2}}{75}$$

Dividing by 75 undoes the multiplication by 75.

$$x=\frac{1900-\lambda ^{2}}{75}$$

Divide -\lambda ^{2}+1900 by 75.

$$x=-\frac{\lambda ^{2}}{75}+\frac{76}{3}$$

Solve for λ (complex solution)

$$\lambda =-5\sqrt{76-3x}$$

$$\lambda =5\sqrt{76-3x}$$

Solve for λ

$$\lambda =5\sqrt{76-3x}$$

$$\lambda =-5\sqrt{76-3x}\text{, }x\leq \frac{76}{3}$$