y+5/2y=-7

Solution for y+5/2y=-7 equation:

y+5/2y=-7

We move all terms to the left:

y+5/2y-(-7)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

y+5/2y+7=0

We multiply all the terms by the denominator


y*2y+7*2y+5=0

Wy multiply elements

2y^2+14y+5=0

a = 2; b = 14; c = +5;
Δ = b2-4ac
Δ = 142-4·2·5
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{39}}{2*2}=\frac{-14-2\sqrt{39}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{39}}{2*2}=\frac{-14+2\sqrt{39}}{4}
$