Question

which equation shows the quadratic formula used correctly to solve $5x^2 + 3x - 4 = 0$ for $x$?

$\boldsymbol{x = \frac{-3 \pm \sqrt{(3)^2 - 4(5)(-4)}}{2(5)}}$

$\boldsymbol{x = \frac{3 \pm \sqrt{(3)^2 + 4(5)(-4)}}{2(5)}}$

$\boldsymbol{x = \frac{3 \pm \sqrt{(3)^2 - 4(5)(-4)}}{2(5)}}$

$\boldsymbol{x = \frac{-3 \pm \sqrt{(3)^2 + 4(5)(-4)}}{2(5)}}$

Explanation:

Step1: Recall Quadratic Formula

The quadratic formula for a quadratic equation \( ax^2 + bx + c = 0 \) is \( x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a} \).

Step2: Identify \( a \), \( b \), \( c \)

For the equation \( 5x^2 + 3x - 4 = 0 \), we have \( a = 5 \), \( b = 3 \), \( c=-4 \).

Step3: Substitute into Formula

Substitute \( a = 5 \), \( b = 3 \), \( c = - 4 \) into the quadratic formula:
\( x=\frac{-3\pm\sqrt{(3)^2-4(5)(-4)}}{2(5)} \) (since \( -b=-3 \), \( b^2=(3)^2 \), \( 4ac = 4\times5\times(-4) \), and \( 2a = 2\times5 \)).

Answer:

\( x=\frac{-3\pm\sqrt{(3)^2 - 4(5)(-4)}}{2(5)} \) (the first option)