Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$3 { x }^{ 2 } -2 \sqrt{ 6x } +2=0$$

Answer

x=0.18403091430664,0.97067031860352

Solution


Separate terms with roots from terms without roots.
\[-2\sqrt{6x}=-3{x}^{2}-2\]
Square both sides.
\[24x=9{x}^{4}+12{x}^{2}+4\]
Move all terms to one side.
\[24x-9{x}^{4}-12{x}^{2}-4=0\]
No root was found algebraically. However, the following root(s) were found by numerical methods.
\[x=0.184031,0.970670\]
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