Solve 0.3a^2-4a+15=p

$$0.3 a ^ { 2 } - 4 a + 15 = p$$

Solve for p

$$p=\frac{3a^{2}}{10}-4a+15$$

Solution Steps

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

$$p=0.3a^{2}-4a+15$$

Solve for a (complex solution)

$$a=\frac{5\sqrt{\frac{6p}{5}-2}+20}{3}$$

$$a=\frac{-5\sqrt{\frac{6p}{5}-2}+20}{3}$$

Solve for a

$$a=\frac{\sqrt{30p-50}+20}{3}$$

$$a=\frac{-\sqrt{30p-50}+20}{3}\text{, }p\geq \frac{5}{3}$$