5/3y+y=72

Solution for 5/3y+y=72 equation:

5/3y+y=72

We move all terms to the left:

5/3y+y-(72)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

y+5/3y-72=0

We multiply all the terms by the denominator


y*3y-72*3y+5=0

Wy multiply elements

3y^2-216y+5=0

a = 3; b = -216; c = +5;
Δ = b2-4ac
Δ = -2162-4·3·5
Δ = 46596
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:

$\sqrt{\Delta}=\sqrt{46596}=\sqrt{4*11649}=\sqrt{4}*\sqrt{11649}=2\sqrt{11649}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-2\sqrt{11649}}{2*3}=\frac{216-2\sqrt{11649}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+2\sqrt{11649}}{2*3}=\frac{216+2\sqrt{11649}}{6}
$