Question

$8x ^{2} + 6x = 5$solve the quadratic equation using the quadratic formula

Answer 1

According to quadratic formula the soluion of th equadaratic equation

$ax^2+bx+c=0$

is given by:

$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

Given data:

We are given th efollowing quadratic equation

$\begin{gathered} 8x^2+6x=5 \\ 8x^2+6x-5=0 \end{gathered}$

Now we have a=8, b=6 and c=-5.

So,

$\begin{gathered} \sqrt[]{b^2-4ac}=\sqrt[]{6^2-4(8)(-5)} \\ =\sqrt[]{36+260} \\ =\sqrt[]{196} \\ =14 \end{gathered}$

So, the solution of the quadaratic equation will be

$x=\frac{-6\pm14}{2(8)}=\frac{-6\pm14}{16}$

So,

$x=\frac{-6+14}{16}=\frac{8}{16}=\frac{1}{2}$

and

$x=\frac{-6-14}{16}=\frac{-20}{16}=-\frac{5}{4}$

So, the solutions are

$x=-\frac{5}{4},x=\frac{1}{2}$

So, the correct option is C).