Question
Solve the following quadratic equation using formula method only
$3 x ^2+2 \sqrt{5} x -5=0$
$3 x ^2+2 \sqrt{5} x -5=0$
✓
Answer
$3 x^2+2 \sqrt{5} x-5=0 $
$ a=3 ; b=2 \sqrt{5} ; c=-5$
$ D=b^2-4 a c $
$=(2 \sqrt{5})^2-4(3)(-5) $
$ =20+60$
$ =80$
$x=\frac{-b \pm \sqrt{b^2-4 ac }}{2 a}$
$ x=\frac{-(2 \sqrt{5}) \pm \sqrt{80}}{6} $
$ x=\frac{-(2 \sqrt{5}) \pm 4 \sqrt{5}}{6} $
$x=\frac{-(2 \sqrt{5}) \pm 4 \sqrt{5}}{6} $
$ x=\frac{-2 \sqrt{5}+4 \sqrt{5}}{6}, x=\frac{-2 \sqrt{5}-4 \sqrt{5}}{6} $
$x=\frac{\sqrt{5}}{3}, x=-\sqrt{5}$
$ a=3 ; b=2 \sqrt{5} ; c=-5$
$ D=b^2-4 a c $
$=(2 \sqrt{5})^2-4(3)(-5) $
$ =20+60$
$ =80$
$x=\frac{-b \pm \sqrt{b^2-4 ac }}{2 a}$
$ x=\frac{-(2 \sqrt{5}) \pm \sqrt{80}}{6} $
$ x=\frac{-(2 \sqrt{5}) \pm 4 \sqrt{5}}{6} $
$x=\frac{-(2 \sqrt{5}) \pm 4 \sqrt{5}}{6} $
$ x=\frac{-2 \sqrt{5}+4 \sqrt{5}}{6}, x=\frac{-2 \sqrt{5}-4 \sqrt{5}}{6} $
$x=\frac{\sqrt{5}}{3}, x=-\sqrt{5}$
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