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3/2y=12y
We move all terms to the left:
3/2y-(12y)=0
Domain of the equation: 2y!=0We add all the numbers together, and all the variables
y!=0/2
y!=0
y∈R
-12y+3/2y=0
We multiply all the terms by the denominator
-12y*2y+3=0
Wy multiply elements
-24y^2+3=0
a = -24; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-24)·3
Δ = 288
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*-24}=\frac{0-12\sqrt{2}}{-48} =-\frac{12\sqrt{2}}{-48} =-\frac{\sqrt{2}}{-4} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*-24}=\frac{0+12\sqrt{2}}{-48} =\frac{12\sqrt{2}}{-48} =\frac{\sqrt{2}}{-4} $
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