2/5y+8y=20

Solution for 2/5y+8y=20 equation:

2/5y+8y=20

We move all terms to the left:

2/5y+8y-(20)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

8y+2/5y-20=0

We multiply all the terms by the denominator


8y*5y-20*5y+2=0

Wy multiply elements

40y^2-100y+2=0

a = 40; b = -100; c = +2;
Δ = b2-4ac
Δ = -1002-4·40·2
Δ = 9680
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:

$\sqrt{\Delta}=\sqrt{9680}=\sqrt{1936*5}=\sqrt{1936}*\sqrt{5}=44\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-44\sqrt{5}}{2*40}=\frac{100-44\sqrt{5}}{80}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+44\sqrt{5}}{2*40}=\frac{100+44\sqrt{5}}{80}
$