Solve x^2-5x^2+6>0

$$x ^ { 2 } - 5 x ^ { 2 } + 6 > 0$$

Solve for x

$$x\in \left(-\frac{\sqrt{6}}{2},\frac{\sqrt{6}}{2}\right)$$

Solution Steps

Combine x^{2} and -5x^{2} to get -4x^{2}.

$$-4x^{2}+6>0$$

Multiply the inequality by -1 to make the coefficient of the highest power in -4x^{2}+6 positive. Since -1 is negative, the inequality direction is changed.

$$4x^{2}-6<0$$

Add \frac{3}{2} to both sides.

$$x^{2}<\frac{3}{2}$$

Calculate the square root of \frac{3}{2} and get \frac{\sqrt{6}}{2}. Rewrite \frac{3}{2} as \left(\frac{\sqrt{6}}{2}\right)^{2}.

$$x^{2}<\left(\frac{\sqrt{6}}{2}\right)^{2}$$

Inequality holds for |x|<\frac{\sqrt{6}}{2}.

$$|x|<\frac{\sqrt{6}}{2}$$

Rewrite |x|<\frac{\sqrt{6}}{2} as x\in \left(-\frac{\sqrt{6}}{2},\frac{\sqrt{6}}{2}\right).

$$x\in \left(-\frac{\sqrt{6}}{2},\frac{\sqrt{6}}{2}\right)$$