1.6y+y-4/15y+116y=21/3

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Solution for 1.6y+y-4/15y+116y=21/3 equation: 



1.6y+y-4/15y+116y=21/3

We move all terms to the left:

1.6y+y-4/15y+116y-(21/3)=0



Domain of the equation: 15y!=0

y!=0/15

y!=0

y∈R



We add all the numbers together, and all the variables

1.6y+y-4/15y+116y-7=0

We add all the numbers together, and all the variables

118.6y-4/15y-7=0

We multiply all the terms by the denominator


(118.6y)*15y-7*15y-4=0

We add all the numbers together, and all the variables

(+118.6y)*15y-7*15y-4=0

We multiply parentheses

1770y^2-7*15y-4=0

Wy multiply elements

1770y^2-105y-4=0

a = 1770; b = -105; c = -4;
Δ = b2-4ac
Δ = -1052-4·1770·(-4)
Δ = 39345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-\sqrt{39345}}{2*1770}=\frac{105-\sqrt{39345}}{3540}
$


$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{39345}}{2*1770}=\frac{105+\sqrt{39345}}{3540}
$

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