2/5y+y=22

Solution for 2/5y+y=22 equation:

2/5y+y=22

We move all terms to the left:

2/5y+y-(22)=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+2/5y-22=0

We multiply all the terms by the denominator


y*5y-22*5y+2=0

Wy multiply elements

5y^2-110y+2=0

a = 5; b = -110; c = +2;
Δ = b2-4ac
Δ = -1102-4·5·2
Δ = 12060
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:

$\sqrt{\Delta}=\sqrt{12060}=\sqrt{36*335}=\sqrt{36}*\sqrt{335}=6\sqrt{335}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-6\sqrt{335}}{2*5}=\frac{110-6\sqrt{335}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+6\sqrt{335}}{2*5}=\frac{110+6\sqrt{335}}{10}
$