4/5y+y=72

Solution for 4/5y+y=72 equation:

4/5y+y=72

We move all terms to the left:

4/5y+y-(72)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

y+4/5y-72=0

We multiply all the terms by the denominator


y*5y-72*5y+4=0

Wy multiply elements

5y^2-360y+4=0

a = 5; b = -360; c = +4;
Δ = b2-4ac
Δ = -3602-4·5·4
Δ = 129520
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:

$\sqrt{\Delta}=\sqrt{129520}=\sqrt{16*8095}=\sqrt{16}*\sqrt{8095}=4\sqrt{8095}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-4\sqrt{8095}}{2*5}=\frac{360-4\sqrt{8095}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+4\sqrt{8095}}{2*5}=\frac{360+4\sqrt{8095}}{10}
$