Solve 3x^2-24*50=0

$$3 { x }^{ 2 } -24 \times 50 = 0$$

Solve for x

$$x=20$$

$$x=-20$$

Steps Using Difference of Squares

Multiply 24 and 50 to get 1200.

$$3x^{2}-1200=0$$

Divide both sides by 3.

$$x^{2}-400=0$$

Consider x^{2}-400. Rewrite x^{2}-400 as x^{2}-20^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-20\right)\left(x+20\right)=0$$

To find equation solutions, solve x-20=0 and x+20=0.

$$x=20 x=-20$$

Steps by Finding Square Root

Multiply 24 and 50 to get 1200.

$$3x^{2}-1200=0$$

Add 1200 to both sides. Anything plus zero gives itself.

$$3x^{2}=1200$$

Divide both sides by 3.

$$x^{2}=\frac{1200}{3}$$

Divide 1200 by 3 to get 400.

$$x^{2}=400$$

Take the square root of both sides of the equation.

$$x=20 x=-20$$

Steps Using the Quadratic Formula

Multiply 24 and 50 to get 1200.

$$3x^{2}-1200=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -1200 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-1200\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-1200\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-1200\right)}}{2\times 3}$$

Multiply -12 times -1200.

$$x=\frac{0±\sqrt{14400}}{2\times 3}$$

Take the square root of 14400.

$$x=\frac{0±120}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±120}{6}$$

Now solve the equation x=\frac{0±120}{6} when ± is plus. Divide 120 by 6.

$$x=20$$

Now solve the equation x=\frac{0±120}{6} when ± is minus. Divide -120 by 6.

$$x=-20$$

The equation is now solved.

$$x=20 x=-20$$