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6x^2/36^x=216
We move all terms to the left:
6x^2/36^x-(216)=0
Domain of the equation: 36^x!=0We multiply all the terms by the denominator
x!=0/1
x!=0
x∈R
6x^2-216*36^x=0
Wy multiply elements
6x^2-7776x=0
a = 6; b = -7776; c = 0;
Δ = b2-4ac
Δ = -77762-4·6·0
Δ = 60466176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{60466176}=7776$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7776)-7776}{2*6}=\frac{0}{12} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7776)+7776}{2*6}=\frac{15552}{12} =1296 $
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