# How do you solve by completing the square for -3x^2 + 8x + 7 = 0?

Jun 10, 2015

Solve:$y = - 3 {x}^{2} + 8 x + 7 = 0$

#### Explanation:

$y = - 3 \left({x}^{2} - \frac{8 x}{3} + \frac{16}{9} - \frac{16}{9} - \frac{7}{3}\right)$

$y = - 3 {\left(x - \frac{4}{3}\right)}^{2} + \frac{16}{3} + 7$

$- 3 {\left(x - \frac{4}{3}\right)}^{2} = - \frac{16}{3} - 7 = - \frac{37}{3}$

${\left(x - \frac{4}{3}\right)}^{2} = \frac{37}{9} \to \left(x - \frac{4}{3}\right) = \pm \frac{\sqrt{37}}{3}$

$x = \frac{4}{3} \pm \frac{\sqrt{37}}{3}$