# How do you solve the quadratic using the quadratic formula given 4x^2+11x=3x-10 over the set of complex numbers?

Oct 24, 2017

Solution: $x \in \left\{- 1 \pm \frac{1}{2} \sqrt{6} i\right\}$

#### Explanation:

$4 {x}^{2} + 11 x = 3 x - 10 \mathmr{and} 4 {x}^{2} + 8 x + 10 = 0$

 a=4 ,b=8 ,c=10 ; D= b^2-4ac=64-160 = -96

Discriminant is negative , so it has complex roots .

Quadratic formula: $x = \frac{- b \pm \sqrt{D}}{2 a}$

$\therefore x = \frac{- 8 \pm \sqrt{- 96}}{8}$ or

$x = \frac{- 8 \pm \sqrt{96} \cdot {i}^{2}}{8} = - 1 \pm \frac{4 \sqrt{6}}{8} i$ or

$x = - 1 \pm \frac{1}{2} \sqrt{6} i$ or

$\therefore x \in \left\{- 1 \pm \frac{1}{2} \sqrt{6} i\right\}$

Solution: $x \in \left\{- 1 \pm \frac{1}{2} \sqrt{6} i\right\}$ [Ans]