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-1/3Y+4Y=6
We move all terms to the left:
-1/3Y+4Y-(6)=0
Domain of the equation: 3Y!=0We add all the numbers together, and all the variables
Y!=0/3
Y!=0
Y∈R
4Y-1/3Y-6=0
We multiply all the terms by the denominator
4Y*3Y-6*3Y-1=0
Wy multiply elements
12Y^2-18Y-1=0
a = 12; b = -18; c = -1;
Δ = b2-4ac
Δ = -182-4·12·(-1)
Δ = 372
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{93}}{2*12}=\frac{18-2\sqrt{93}}{24} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{93}}{2*12}=\frac{18+2\sqrt{93}}{24} $
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