Solve the following equation for x and give your answer correct to two decimal places :

4x² - 5x - 3 = 0

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

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

We know that,

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

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

$\Rightarrow x = \dfrac{-(-5) \pm \sqrt{(-5)^2 - 4.(4).(-3)}}{2(4)} \\[1em] = \dfrac{5 \pm \sqrt{25 + 48}}{8} \\[1em] = \dfrac{5 \pm \sqrt{73}}{8} \\[1em] = \dfrac{5 \pm 8.54}{8} \\[1em] = \dfrac{5 + 8.54}{8} \text{ and } \dfrac{5 - 8.54}{8} \\[1em] = \dfrac{13.54}{8} \text{ and } \dfrac{-3.54}{8} \\[1em] = 1.69 \text{ and } -0.44$

Hence, x = 1.69 and -0.44