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1/3y+y=68
We move all terms to the left:
1/3y+y-(68)=0
Domain of the equation: 3y!=0We add all the numbers together, and all the variables
y!=0/3
y!=0
y∈R
y+1/3y-68=0
We multiply all the terms by the denominator
y*3y-68*3y+1=0
Wy multiply elements
3y^2-204y+1=0
a = 3; b = -204; c = +1;
Δ = b2-4ac
Δ = -2042-4·3·1
Δ = 41604
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{41604}=\sqrt{4*10401}=\sqrt{4}*\sqrt{10401}=2\sqrt{10401}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-204)-2\sqrt{10401}}{2*3}=\frac{204-2\sqrt{10401}}{6} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-204)+2\sqrt{10401}}{2*3}=\frac{204+2\sqrt{10401}}{6} $
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