Solve sqrt{5}p^2-5sqrt{3}p+q=0

$$\sqrt { 5 } p ^ { 2 } - 5 \sqrt { 3 } p + q = 0$$

Solve for q

$$q=-p\left(\sqrt{5}p-5\sqrt{3}\right)$$

Solution Steps

Subtract \sqrt{5}p^{2}-5\sqrt{3}p from both sides. Anything subtracted from zero gives its negation.

$$q=-\left(\sqrt{5}p^{2}-5\sqrt{3}p\right)$$

To find the opposite of \sqrt{5}p^{2}-5\sqrt{3}p, find the opposite of each term.

$$q=-\sqrt{5}p^{2}+5\sqrt{3}p$$

Solve for p

$$p=\frac{\sqrt{-20\sqrt{5}q+375}+5\sqrt{15}}{10}$$

$$p=\frac{-\sqrt{-20\sqrt{5}q+375}+5\sqrt{15}}{10}\text{, }q\leq \frac{15\sqrt{5}}{4}$$