Solve 20x-4x^2-25<0

$$20 x - 4 x ^ { 2 } - 25 < 0$$

Solve for x

$$x\neq \frac{5}{2}$$

Steps Using the Quadratic Formula

Multiply the inequality by -1 to make the coefficient of the highest power in 20x-4x^{2}-25 positive. Since -1 is negative, the inequality direction is changed.

$$-20x+4x^{2}+25>0$$

To solve the inequality, factor the left hand side. Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$-20x+4x^{2}+25=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 4 for a, -20 for b, and 25 for c in the quadratic formula.

$$x=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\times 4\times 25}}{2\times 4}$$

Do the calculations.

$$x=\frac{20±0}{8}$$

Solutions are the same.

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

Rewrite the inequality by using the obtained solutions.

$$4\left(x-\frac{5}{2}\right)^{2}>0$$

Inequality holds for x\neq \frac{5}{2}.

$$x\neq \frac{5}{2}$$