Solve 2x^2-5x^2+5=0

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

Solve for x

$$x = \frac{\sqrt{15}}{3} \approx 1.290994449$$

$$x = -\frac{\sqrt{15}}{3} \approx -1.290994449$$

Steps by Finding Square Root

Combine 2x^{2} and -5x^{2} to get -3x^{2}.

$$-3x^{2}+5=0$$

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$-3x^{2}=-5$$

Divide both sides by -3.

$$x^{2}=\frac{-5}{-3}$$

Fraction \frac{-5}{-3} can be simplified to \frac{5}{3} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{5}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{15}}{3} x=-\frac{\sqrt{15}}{3}$$

Steps Using the Quadratic Formula

Combine 2x^{2} and -5x^{2} to get -3x^{2}.

$$-3x^{2}+5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 0 for b, and 5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)\times 5}}{2\left(-3\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3\right)\times 5}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\times 5}}{2\left(-3\right)}$$

Multiply 12 times 5.

$$x=\frac{0±\sqrt{60}}{2\left(-3\right)}$$

Take the square root of 60.

$$x=\frac{0±2\sqrt{15}}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{0±2\sqrt{15}}{-6}$$

Now solve the equation x=\frac{0±2\sqrt{15}}{-6} when ± is plus.

$$x=-\frac{\sqrt{15}}{3}$$

Now solve the equation x=\frac{0±2\sqrt{15}}{-6} when ± is minus.

$$x=\frac{\sqrt{15}}{3}$$

The equation is now solved.

$$x=-\frac{\sqrt{15}}{3} x=\frac{\sqrt{15}}{3}$$