Question

9s² – 4 = –6s

Answer 1

Given: 9s² – 4 = –6s
On rewriting this equation in the standard form of the quadratic equation, we get:
9s² + 6s – 4 = 0
On comparing this equation with ax² + bx + c = 0, we get:
a = 9, b = 6 and c = –4
Here, the variable of the quadratic equation is 's'.
For the quadratic equation ax² + bx + c = 0, we know that the quadratic formula is
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
On substituting a = 9, b = 6 and c = –4, we get:
$$\begin{gathered} s=\frac{-6\pm \sqrt{6^2-4\times 9\times \left(-4\right)}}{2\times 9} \\ =\frac{-6\pm \sqrt{36+144}}{18} \\ =\frac{-6\pm \sqrt{180}}{18} \\ =\frac{-6\pm 6\sqrt{5}}{18} \\ =\frac{6\left(-1\pm \sqrt{5}\right)}{18} \\ =\frac{-1\pm \sqrt{5}}{3} \end{gathered}$$
Thus, the solution of the given quadratic equation is s = $\frac{-1+\sqrt{5}}{3},\frac{-1-\sqrt{5}}{3}$.