Question

Solve y = 5x2 - 6x - 9 using the quadratic formula.

Answer 1

Given:

$y=5x^2-6x-9$

Let y=0

$5x^2-6x-2=0$

From the above expression let, a=5, b=-6 and c=2.

The expression to solve the quadratic equation is,

$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

Substitute values in the above expression.

$\begin{gathered} x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4\times5\times(-2)}}{2\times5} \\ x=\frac{6\pm\sqrt[]{36+40}}{10} \\ x=\frac{6\pm\sqrt[]{76}}{10} \\ x=\frac{6\pm2\sqrt[]{19}}{10} \\ x=\frac{3\pm\sqrt[]{19}}{5} \end{gathered}$

From the above expression the values of x is,

$\begin{gathered} x=\frac{3+\sqrt[]{19}}{5}=1.472 \\ OR \\ x=\frac{3-\sqrt[]{19}}{5}=-0.272 \end{gathered}$