which equation shows the quadratic formula used correctly to solve \( 5x^2 + 3x – 4 = 0 \) for x?
Equation is \( 5x^2 + 3x – 4 = 0 \) [Convert Equation to quadratic equation to find the value of x through quadratic formula]
\( 5x^2 + 3x + (-4) = 0 \) [According to the Quadratic Equation a= 5, b= 3 and c=-4]
Quadratic Formula \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\) [put the value of a, b, and c in the formula]
=> \(x = {-3 \pm \sqrt{3^2-4\times 5 \times (-4)} \over 2 \times 5}\)
=> \(x = {-3 \pm \sqrt{9+80} \over 10}\)
=> \(x = {-3 \pm \sqrt{89} \over 10}\) [ the value of \( \sqrt{89} = 9.434 \) ]
=> \(x = {-3 \pm 9.434 \over 10}\)
=> \(x = \frac{-3 – 9.434}{10} \;or\; \frac{-3 + 9.434}{10} \)
=> \(x = \frac{-12.434}{10} \;or\; \frac{6.434}{10} \)
=> \(x = -1.2434 \;or\; 0.6434 \)