The given equation is :
[tex]24x^{3}y^{2} -4x^{2}y +84x^{4}[/tex]
Now taking [tex]4x^{2}[/tex] common from all the terms, we get
[tex]4x^{2} (6xy^{2} -y+21x^{2} )=0[/tex]
Writing the equation in standard form we get:
[tex]21x^{2} +6xy^{2} -y=0[/tex]
Now we will use the formula of quadratic equations to solve this,
[tex]x1,2 = \frac{-b+\sqrt{b^{2}-4ac }} {2a}[/tex] and
[tex]x1,2 = \frac{-b-\sqrt{b^{2}-4ac }} {2a}[/tex]
Now putting a = 21, b = 6y² and c = -y and solving the equations, we get
[tex]x=\frac{-6y^{2}+\sqrt{36y^{4}+84y }}{42}[/tex] and
[tex]x=\frac{-6y^{2}-\sqrt{36y^{4}+84y }}{42}[/tex]
