Solve 0=1.5-10x^2/2

$$0=1.5- \frac{ 10 { x }^{ 2 } }{ 2 }$$

Solve for x

$$x=\frac{\sqrt{30}}{10}\approx 0.547722558$$

$$x=-\frac{\sqrt{30}}{10}\approx -0.547722558$$

Steps by Finding Square Root

Multiply both sides of the equation by 2.

$$0=3-10x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$3-10x^{2}=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$-10x^{2}=-3$$

Divide both sides by -10.

$$x^{2}=\frac{-3}{-10}$$

Fraction \frac{-3}{-10} can be simplified to \frac{3}{10} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{3}{10}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{30}}{10} x=-\frac{\sqrt{30}}{10}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

$$0=3-10x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$3-10x^{2}=0$$

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.

$$-10x^{2}+3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -10 for a, 0 for b, and 3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-10\right)\times 3}}{2\left(-10\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-10\right)\times 3}}{2\left(-10\right)}$$

Multiply -4 times -10.

$$x=\frac{0±\sqrt{40\times 3}}{2\left(-10\right)}$$

Multiply 40 times 3.

$$x=\frac{0±\sqrt{120}}{2\left(-10\right)}$$

Take the square root of 120.

$$x=\frac{0±2\sqrt{30}}{2\left(-10\right)}$$

Multiply 2 times -10.

$$x=\frac{0±2\sqrt{30}}{-20}$$

Now solve the equation x=\frac{0±2\sqrt{30}}{-20} when ± is plus.

$$x=-\frac{\sqrt{30}}{10}$$

Now solve the equation x=\frac{0±2\sqrt{30}}{-20} when ± is minus.

$$x=\frac{\sqrt{30}}{10}$$

The equation is now solved.

$$x=-\frac{\sqrt{30}}{10} x=\frac{\sqrt{30}}{10}$$