Question
Solve the quadratic equation:
$4 \sqrt{5} x^2+7 x-3 \sqrt{5}=0$
$4 \sqrt{5} x^2+7 x-3 \sqrt{5}=0$
✓
Answer
The given equation is
$4 \sqrt{5} x^2+7 x-3 \sqrt{5}=0 . $
$\Rightarrow 4 \sqrt{5} x^2+12 x-5 x-3 \sqrt{5}=0 $
$\Rightarrow 4 x(\sqrt{5} x+3)-\sqrt{5}(\sqrt{5} x+3)=0 $
$\Rightarrow(\sqrt{5} x+3)(4 x-\sqrt{5})=0 $
$\Rightarrow \sqrt{5} x+3=0 \text { or } 4 x-\sqrt{5}=0 $
$\Rightarrow \sqrt{5} x=-3 \text { and } 4 x=\sqrt{5}$
$\Rightarrow x =-\frac{3}{\sqrt{5}} \text { and } x=\frac{\sqrt{5}}{4} $
$ \text { so } x =-\frac{3}{\sqrt{5}}, \frac{\sqrt{5}}{4}$
$4 \sqrt{5} x^2+7 x-3 \sqrt{5}=0 . $
$\Rightarrow 4 \sqrt{5} x^2+12 x-5 x-3 \sqrt{5}=0 $
$\Rightarrow 4 x(\sqrt{5} x+3)-\sqrt{5}(\sqrt{5} x+3)=0 $
$\Rightarrow(\sqrt{5} x+3)(4 x-\sqrt{5})=0 $
$\Rightarrow \sqrt{5} x+3=0 \text { or } 4 x-\sqrt{5}=0 $
$\Rightarrow \sqrt{5} x=-3 \text { and } 4 x=\sqrt{5}$
$\Rightarrow x =-\frac{3}{\sqrt{5}} \text { and } x=\frac{\sqrt{5}}{4} $
$ \text { so } x =-\frac{3}{\sqrt{5}}, \frac{\sqrt{5}}{4}$
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