Solve 6p^2-8p+6=a

$$6 p ^ { 2 } - 8 p + 6 = a$$

Solve for a

$$a=6p^{2}-8p+6$$

Solution Steps

Swap sides so that all variable terms are on the left hand side.

$$a=6p^{2}-8p+6$$

Solve for p (complex solution)

$$p=\frac{\sqrt{6a-20}}{6}+\frac{2}{3}$$

$$p=-\frac{\sqrt{6a-20}}{6}+\frac{2}{3}$$

Solve for p

$$p=\frac{\sqrt{6a-20}}{6}+\frac{2}{3}$$

$$p=-\frac{\sqrt{6a-20}}{6}+\frac{2}{3}\text{, }a\geq \frac{10}{3}$$