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})+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})+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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