Question

2*​x^​2-​4*​x-3=0
solve for x​

Answer 1

Step-by-step explanation:

I hope you understand...

Answer 2

$2x^2-4x-3=0$

Quadratic equation : quadratic formula.

$x=\frac{-b'\pm \sqrt{b'^2-ac} }{a}$ are the roots of a quadratic equation $ax^2+2b'x+c=0$.

$2b'$ stands for an even coefficient of a linear term.

$x=\frac{2\pm \sqrt{4+6} }{2}$

∴ $x=\frac{2\pm \sqrt{10} }{2}$

---------- QUADRATIC FORMULA FOR $ax^2+2b'x+c=0$ ----------

Apply quadratic formula first.

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

$=\frac{-2b'\pm 2\sqrt{b'^2-ac} }{2a}$

$=\frac{-b'\pm \sqrt{b'2-ac} }{a}$

∴ $x=\frac{-b'\pm \sqrt{b'^2-ac} }{a}$ are the roots of a quadratic equation $ax^2+2b'x+c=0$.