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72(2/9)*2y=12
We move all terms to the left:
72(2/9)*2y-(12)=0
Domain of the equation: 9)*2y!=0We add all the numbers together, and all the variables
y!=0/1
y!=0
y∈R
72(+2/9)*2y-12=0
We multiply parentheses
288y^2-12=0
a = 288; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·288·(-12)
Δ = 13824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{13824}=\sqrt{2304*6}=\sqrt{2304}*\sqrt{6}=48\sqrt{6}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{6}}{2*288}=\frac{0-48\sqrt{6}}{576} =-\frac{48\sqrt{6}}{576} =-\frac{\sqrt{6}}{12} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{6}}{2*288}=\frac{0+48\sqrt{6}}{576} =\frac{48\sqrt{6}}{576} =\frac{\sqrt{6}}{12} $
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