2/5y+y-4=31

Solution for 2/5y+y-4=31 equation:

2/5y+y-4=31

We move all terms to the left:

2/5y+y-4-(31)=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-35=0

We multiply all the terms by the denominator


y*5y-35*5y+2=0

Wy multiply elements

5y^2-175y+2=0

a = 5; b = -175; c = +2;
Δ = b2-4ac
Δ = -1752-4·5·2
Δ = 30585
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{-(-175)-\sqrt{30585}}{2*5}=\frac{175-\sqrt{30585}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-175)+\sqrt{30585}}{2*5}=\frac{175+\sqrt{30585}}{10}
$