# How do you solve 18x^2+10x=-3x+21?

May 26, 2017

$\frac{7}{9} \mathmr{and} - \frac{3}{2}$

#### Explanation:

Use the new Transforming Method (Socratic Search):
$y = 18 {x}^{2} + 13 x - 21 = 0$
Transformed equation: $y ' = {x}^{2} + 13 x - 378 = 0$
Method: Find 2 real roots of y', then, divide them by a = 18.
Compose factor pairs of (ac = - 378), using a calculator.
...(6 - 18)(7, - 34)(14, - 27). This last sum is (-13 = - b). Then, the 2 real roots of y' are: 14 and - 27.
Back to y, its 2 real roots are:
$x 1 = \frac{14}{a} = \frac{14}{18} = \frac{7}{9}$, and $x 2 = - \frac{27}{a} = - \frac{27}{18} = - \frac{3}{2}$
Answers: $\frac{7}{9} \mathmr{and} - \frac{3}{2}$