Question

What is the positive solution to 2x2 -4x -30.=0 ?

Answer 1

Answer:

$x=1+\frac{\sqrt[]{40}}{4}$

Explanation: Given the folllowing equation, we need its positive solution or root:

$2x^2-4x-30=0$

Solution by Quadratic formula:

$x=\frac{-B\pm\sqrt[]{B^6-4AC}}{2S}\rightarrow(1)$

Where x can be positive and negative, but we are interested in the positive solution.

Constants A B C in (1) are as follows:

$\begin{gathered} A=2 \\ B=-4 \\ C=-30 \end{gathered}$

Plugging these values in (1) gives us:

$x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(2)(-30)}}{2(2)}=\frac{4\pm\sqrt[]{16+(8)(30}}{4}$

Firther simplification gives:

$\begin{gathered} x=\frac{4\pm\sqrt[]{16+24}}{4}=\frac{4\pm\sqrt[]{40}}{4}\rightarrow positive\rightarrow x=\frac{4+\sqrt[]{40}}{4}=1+\frac{\sqrt[]{40}}{4} \\ \therefore\rightarrow \\ x=1+\frac{\sqrt[]{40}}{4} \end{gathered}$