Solve Using the Quadratic Formula 5x^2-9x+4=0

$5 x^{2} - 9 x + 4 = 0$

Step 1

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 2

Substitute the values $a = 5$ , $b = - 9$ , and $c = 4$ into the quadratic formula and solve for $x$ .

$\frac{9 \pm \sqrt{{(- 9)}^{2} - 4 \cdot (5 \cdot 4)}}{2 \cdot 5}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 9$ to the power of $2$ .

$x = \frac{9 \pm \sqrt{81 - 4 \cdot 5 \cdot 4}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot 4$ .

Multiply $- 4$ by $5$ .

$x = \frac{9 \pm \sqrt{81 - 20 \cdot 4}}{2 \cdot 5}$

Multiply $- 20$ by $4$ .

$x = \frac{9 \pm \sqrt{81 - 80}}{2 \cdot 5}$

Subtract $80$ from $81$ .

$x = \frac{9 \pm \sqrt{1}}{2 \cdot 5}$

Any root of $1$ is $1$ .

$x = \frac{9 \pm 1}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{9 \pm 1}{10}$

Step 4

The final answer is the combination of both solutions.

$x = 1, \frac{4}{5}$