To solve the quadratic equation [tex]\(5x^2 + 3x - 4 = 0\)[/tex], we can use the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
For the given quadratic equation, the coefficients are:
- [tex]\(a = 5\)[/tex]
- [tex]\(b = 3\)[/tex]
- [tex]\(c = -4\)[/tex]
Substitute these values into the quadratic formula:
[tex]\[ x = \frac{-3 \pm \sqrt{3^2 - 4 \cdot 5 \cdot (-4)}}{2 \cdot 5} \][/tex]
Simplify inside the square root:
[tex]\[ x = \frac{-3 \pm \sqrt{9 + 80}}{10} \][/tex]
[tex]\[ x = \frac{-3 \pm \sqrt{89}}{10} \][/tex]
Therefore, the correct formula being used is:
[tex]\[ x = \frac{-3 \pm \sqrt{(3)^2 - 4(5)(-4)}}{2(5)} \][/tex]
So, the correct answer from the given options is:
[tex]\[ x = \frac{-3 \pm \sqrt{(3)^2 - 4(5)(-4)}}{2(5)} \][/tex]
