y-5/6y+2=10

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Solution for y-5/6y+2=10 equation:



y-5/6y+2=10
We move all terms to the left:
y-5/6y+2-(10)=0
Domain of the equation: 6y!=0
y!=0/6
y!=0
y∈R
We add all the numbers together, and all the variables
y-5/6y-8=0
We multiply all the terms by the denominator
y*6y-8*6y-5=0
Wy multiply elements
6y^2-48y-5=0
a = 6; b = -48; c = -5;
Δ = b2-4ac
Δ = -482-4·6·(-5)
Δ = 2424
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:
$\sqrt{\Delta}=\sqrt{2424}=\sqrt{4*606}=\sqrt{4}*\sqrt{606}=2\sqrt{606}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{606}}{2*6}=\frac{48-2\sqrt{606}}{12} $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{606}}{2*6}=\frac{48+2\sqrt{606}}{12} $

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