How do you solve -12x^2 + 5x +2=0 using the quadratic formula?

${x}_{1} = - \frac{1}{4} \text{ }$and ${x}_{2} = \frac{2}{3}$

Explanation:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Let $a = - 12$ and $b = 5$ and $c = 2$

$y = \frac{- 5 \pm \sqrt{{\left(5\right)}^{2} - 4 \cdot \left(- 12\right) \cdot \left(2\right)}}{2 \left(- 12\right)}$

$y = \frac{- 5 \pm \sqrt{25 + 96}}{- 24}$

$y = \frac{- 5 \pm \sqrt{121}}{- 24}$

${y}_{1} = \frac{- 5 + 11}{- 24} = \frac{6}{-} 24 = - \frac{1}{4}$

${y}_{2} = \frac{- 5 - 11}{- 24} = - \frac{16}{- 24} = \frac{2}{3}$

God bless.... I hope the explanation is useful.