Solve Using the Quadratic Formula 4x^2-15x+14=0

$4 x^{2} - 15 x + 14 = 0$

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 $a = 4$ , $b = - 15$ , and $c = 14$ into the quadratic formula and solve for $x$ .

$\frac{15 \pm \sqrt{{(- 15)}^{2} - 4 \cdot (4 \cdot 14)}}{2 \cdot 4}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 15$ to the power of $2$ .

$x = \frac{15 \pm \sqrt{225 - 4 \cdot 4 \cdot 14}}{2 \cdot 4}$

Multiply $- 4 \cdot 4 \cdot 14$ .

Multiply $- 4$ by $4$ .

$x = \frac{15 \pm \sqrt{225 - 16 \cdot 14}}{2 \cdot 4}$

Multiply $- 16$ by $14$ .

$x = \frac{15 \pm \sqrt{225 - 224}}{2 \cdot 4}$

Subtract $224$ from $225$ .

$x = \frac{15 \pm \sqrt{1}}{2 \cdot 4}$

Any root of $1$ is $1$ .

$x = \frac{15 \pm 1}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{15 \pm 1}{8}$

Step 4

The final answer is the combination of both solutions.

$x = 2, \frac{7}{4}$