Solve 5x^2-15=0

$$5 x ^ { 2 } - 15 = 0$$

Solve for x

$$x=\sqrt{3}\approx 1.732050808$$

$$x=-\sqrt{3}\approx -1.732050808$$

Steps by Finding Square Root

Add 15 to both sides. Anything plus zero gives itself.

$$5x^{2}=15$$

Divide both sides by 5.

$$x^{2}=\frac{15}{5}$$

Divide 15 by 5 to get 3.

$$x^{2}=3$$

Take the square root of both sides of the equation.

$$x=\sqrt{3} x=-\sqrt{3}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$5x^{2}-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-15\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-15\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-15\right)}}{2\times 5}$$

Multiply -20 times -15.

$$x=\frac{0±\sqrt{300}}{2\times 5}$$

Take the square root of 300.

$$x=\frac{0±10\sqrt{3}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±10\sqrt{3}}{10}$$

Now solve the equation x=\frac{0±10\sqrt{3}}{10} when ± is plus.

$$x=\sqrt{3}$$

Now solve the equation x=\frac{0±10\sqrt{3}}{10} when ± is minus.

$$x=-\sqrt{3}$$

The equation is now solved.

$$x=\sqrt{3} x=-\sqrt{3}$$