9/2y+12+4y=-5

Solution for 9/2y+12+4y=-5 equation:

9/2y+12+4y=-5

We move all terms to the left:

9/2y+12+4y-(-5)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

4y+9/2y+17=0

We multiply all the terms by the denominator


4y*2y+17*2y+9=0

Wy multiply elements

8y^2+34y+9=0

a = 8; b = 34; c = +9;
Δ = b2-4ac
Δ = 342-4·8·9
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{217}}{2*8}=\frac{-34-2\sqrt{217}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{217}}{2*8}=\frac{-34+2\sqrt{217}}{16}
$