Question

Quadratic Formula and the two solutions I would get

Answer 1

A quadratic equation is given by three parameters:

$ax^2+bx+c=0$

• a is the quadratic coefficient, since it multiplies $x^2$
• b is the linear coefficient, since it multiplies $x$
• c is the numeric coefficient, since it's a pure number.

The quadratic formula states that the two (possible) solutions for a quadratic equation are

$ax^2+bx+c=0 \iff x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

In your case, you have

$a=8,\quad b=-10,\quad c=-1$

So, your quadratic equation and its solving formula become

$8x^2-10x-1=0 \iff x_{1,2} = \dfrac{10\pm\sqrt{100+32}}{16}=\dfrac{10\pm\sqrt{132}}{16}$