Solve -4x^2+81<0

$$- 4 x ^ { 2 } + 81 < 0$$

Solve for x

$$x\in \left(-\infty,-\frac{9}{2}\right)\cup \left(\frac{9}{2},\infty\right)$$

Solution Steps

Multiply the inequality by -1 to make the coefficient of the highest power in -4x^{2}+81 positive. Since -1 is negative, the inequality direction is changed.

$$4x^{2}-81>0$$

Add \frac{81}{4} to both sides.

$$x^{2}>\frac{81}{4}$$

Calculate the square root of \frac{81}{4} and get \frac{9}{2}. Rewrite \frac{81}{4} as \left(\frac{9}{2}\right)^{2}.

$$x^{2}>\left(\frac{9}{2}\right)^{2}$$

Inequality holds for |x|>\frac{9}{2}.

$$|x|>\frac{9}{2}$$

Rewrite |x|>\frac{9}{2} as x<-\frac{9}{2}\text{; }x>\frac{9}{2}.

$$x<-\frac{9}{2}\text{; }x>\frac{9}{2}$$