Solve the following equation and give your answer correct to 3 significant figures :

5x² - 3x - 4 = 0

Comparing 5x² - 3x - 4 = 0 with ax² + bx + c = 0 we get,

a = 5, b = -3 and c = -4.

We know that,

x = $\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Substituting values of a, b and c in above equation we get,

$\Rightarrow x = \dfrac{-(-3) \pm \sqrt{(-3)^2 - 4.(5).(-4)}}{2(5)} \\[1em] = \dfrac{3 \pm \sqrt{9 + 80}}{10} \\[1em] = \dfrac{3 \pm \sqrt{89}}{10} \\[1em] = \dfrac{3 \pm 9.434}{10} \\[1em] = \dfrac{3 + 9.434}{10} \text{ or } \dfrac{3 - 9.434}{10} \\[1em] = \dfrac{12.434}{10} \text{ or } \dfrac{-6.434}{10} \\[1em] = 1.2434 \text{ or } -0.6434 \\[1em] \approx 1.243 \text{ or } -0.643$

Hence, x = 1.243 or -0.643