2/y+4y=-7

Solution for 2/y+4y=-7 equation:

2/y+4y=-7

We move all terms to the left:

2/y+4y-(-7)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

4y+2/y+7=0

We multiply all the terms by the denominator


4y*y+7*y+2=0

We add all the numbers together, and all the variables

7y+4y*y+2=0

Wy multiply elements

4y^2+7y+2=0

a = 4; b = 7; c = +2;
Δ = b2-4ac
Δ = 72-4·4·2
Δ = 17
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{-(7)-\sqrt{17}}{2*4}=\frac{-7-\sqrt{17}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{17}}{2*4}=\frac{-7+\sqrt{17}}{8}
$