3/5y+2y=8

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Solution for 3/5y+2y=8 equation:



3/5y+2y=8
We move all terms to the left:
3/5y+2y-(8)=0
Domain of the equation: 5y!=0
y!=0/5
y!=0
y∈R
We add all the numbers together, and all the variables
2y+3/5y-8=0
We multiply all the terms by the denominator
2y*5y-8*5y+3=0
Wy multiply elements
10y^2-40y+3=0
a = 10; b = -40; c = +3;
Δ = b2-4ac
Δ = -402-4·10·3
Δ = 1480
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:
$\sqrt{\Delta}=\sqrt{1480}=\sqrt{4*370}=\sqrt{4}*\sqrt{370}=2\sqrt{370}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{370}}{2*10}=\frac{40-2\sqrt{370}}{20} $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{370}}{2*10}=\frac{40+2\sqrt{370}}{20} $

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