-14/3y+60+2y=0

Solution for -14/3y+60+2y=0 equation:

-14/3y+60+2y=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

2y-14/3y+60=0

We multiply all the terms by the denominator


2y*3y+60*3y-14=0

Wy multiply elements

6y^2+180y-14=0

a = 6; b = 180; c = -14;
Δ = b2-4ac
Δ = 1802-4·6·(-14)
Δ = 32736
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:

$\sqrt{\Delta}=\sqrt{32736}=\sqrt{16*2046}=\sqrt{16}*\sqrt{2046}=4\sqrt{2046}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-4\sqrt{2046}}{2*6}=\frac{-180-4\sqrt{2046}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+4\sqrt{2046}}{2*6}=\frac{-180+4\sqrt{2046}}{12}
$