3/5y+y=8

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

3/5y+y=8

We move all terms to the left:

3/5y+y-(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

y+3/5y-8=0

We multiply all the terms by the denominator


y*5y-8*5y+3=0

Wy multiply elements

5y^2-40y+3=0

a = 5; b = -40; c = +3;
Δ = b2-4ac
Δ = -402-4·5·3
Δ = 1540
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:

$\sqrt{\Delta}=\sqrt{1540}=\sqrt{4*385}=\sqrt{4}*\sqrt{385}=2\sqrt{385}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{385}}{2*5}=\frac{40-2\sqrt{385}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{385}}{2*5}=\frac{40+2\sqrt{385}}{10}
$