# How do you solve the quadratic using the quadratic formula given 10x^2+9=x?

Aug 31, 2016

$x = \frac{1}{20} - i \frac{\sqrt{359}}{20}$ or $\frac{1}{20} + i \frac{\sqrt{359}}{20}$

#### Explanation:

Quadratic formula gives the solution of quadratic equation $a {x}^{2} + b x + c = 0$ as

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

Hence solution of the equation $10 {x}^{2} + 9 = x$ which can also be written in general form as $10 {x}^{2} - x + 9 = 0$ is

x=(-(-1)+-sqrt((-1)^2-4×10×9))/(2×10)

= $\frac{1 \pm \sqrt{1 - 360}}{20}$

= $\frac{1}{20} \pm i \frac{\sqrt{359}}{20}$

i.e. $x = \frac{1}{20} - i \frac{\sqrt{359}}{20}$ or

$\frac{1}{20} + i \frac{\sqrt{359}}{20}$