3/2y+y=55

Solution for 3/2y+y=55 equation:

3/2y+y=55

We move all terms to the left:

3/2y+y-(55)=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+3/2y-55=0

We multiply all the terms by the denominator


y*2y-55*2y+3=0

Wy multiply elements

2y^2-110y+3=0

a = 2; b = -110; c = +3;
Δ = b2-4ac
Δ = -1102-4·2·3
Δ = 12076
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:

$\sqrt{\Delta}=\sqrt{12076}=\sqrt{4*3019}=\sqrt{4}*\sqrt{3019}=2\sqrt{3019}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-2\sqrt{3019}}{2*2}=\frac{110-2\sqrt{3019}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+2\sqrt{3019}}{2*2}=\frac{110+2\sqrt{3019}}{4}
$