# How do you use the quadratic formula to solve 2/3x^2-2=1/2x+1?

Jul 25, 2017

$x = 1.921$

$x = - 1.171$

#### Explanation:

$\frac{2}{3} {x}^{2} - 2 = \frac{1}{2} x + 1 \text{ } \leftarrow$ get rid of the fractions: $\times 6$

$\frac{{\cancel{6}}^{2} \times 2}{\cancel{3}} {x}^{2} - 6 \times 2 = \frac{{\cancel{6}}^{3} \times 1}{\cancel{2}} x + 6 \times 1$

$4 {x}^{2} - 12 = 3 x + 6 \text{ } \leftarrow$ make it equal to $0$

$4 {x}^{2} - 3 x - 18 = 0 \text{ } \leftarrow$ does not factorise

Use the quadratic formula to solve for $x$

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a} \text{ }$ with $a = 4 , b = - 3 \mathmr{and} c = - 18$

$x = \frac{- \left(- 3\right) \pm \sqrt{{\left(- 3\right)}^{2} - 4 \left(4\right) \left(- 18\right)}}{2 \left(4\right)}$

$x = \frac{3 \pm \sqrt{\left(9 + 144\right)}}{8}$

$x = \frac{3 \pm \sqrt{153}}{8}$

Solve twice to find $x$

$x = 1.921$

$x = - 1.171$