# How do you solve 4x^2-13x+3=0?

Jul 15, 2015

$x = \frac{1}{4} , 3$

#### Explanation:

$4 {x}^{2} - 13 x + 3 = 0$ is a quadratic equation with the form $a {x}^{2} + b x + c = 0$, where $a = 4 ,$ $b = - 13 ,$ and $c = 3$.

Use the quadratic formula.

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

$x = \frac{- \left(- 13\right) \pm \sqrt{- {13}^{2} - 4 \cdot 4 \cdot 3}}{2 \cdot 4}$ =

$x = \frac{13 \pm \sqrt{169 - 48}}{8}$ =

$x = \frac{13 \pm \sqrt{121}}{8}$ =

$x = \frac{13 \pm 11}{8}$

Solve for $x$.

$x = \frac{13 + 11}{8} = \frac{24}{8} = 3$

$x = \frac{13 - 11}{8} = \frac{2}{8} = \frac{1}{4}$

Jul 16, 2015

Solve: y = 4x^2 - 13x + 3 = 0
Answers: 1/4 and 3

#### Explanation:

Use the new Transforming Method (Google and Yahoo Search)
Transformed equation: y' = x^2 - 13x + 12. Both roots are positive.
Factor pairs of ac = 12 --> (1, 12) = 13.
y1 = 1 and y2 = 12
x1 = y1/a = 1/4 and x2 = y2/a = 12/4 = 3
Answers: 1/4 and 3.

Note : I advise students to learn and solve quadratic equations by the new Transforming Method. It is simpler and faster than using the formula or the factoring by grouping method.