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2/3y+1=16y+8
We move all terms to the left:
2/3y+1-(16y+8)=0
Domain of the equation: 3y!=0We get rid of parentheses
y!=0/3
y!=0
y∈R
2/3y-16y-8+1=0
We multiply all the terms by the denominator
-16y*3y-8*3y+1*3y+2=0
Wy multiply elements
-48y^2-24y+3y+2=0
We add all the numbers together, and all the variables
-48y^2-21y+2=0
a = -48; b = -21; c = +2;
Δ = b2-4ac
Δ = -212-4·(-48)·2
Δ = 825
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{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-5\sqrt{33}}{2*-48}=\frac{21-5\sqrt{33}}{-96}y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+5\sqrt{33}}{2*-48}=\frac{21+5\sqrt{33}}{-96}
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