# How do you solve -4x^2+19x=-30?

Feb 1, 2017

$x = 6$ or $x = - \frac{5}{4}$

#### Explanation:

Bring the equation to standard form:
y = 4x^2 - 19x - 30 = 0
Use the improved quadratic formula (Socratic Search)
$D = {d}^{2} = {b}^{2} - 4 a c = 361 + 480 = 841$ --> $d = \pm 29$
There are 2 real roots:
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = \frac{19}{8} \pm \frac{29}{8}$
$x = \frac{19 \pm 29}{8}$

i.e. $x = 6$ or $x = - \frac{5}{4}$