4/5y+116+y+10=180

Solution for 4/5y+116+y+10=180 equation:

4/5y+116+y+10=180

We move all terms to the left:

4/5y+116+y+10-(180)=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-54=0

We multiply all the terms by the denominator


y*5y-54*5y+4=0

Wy multiply elements

5y^2-270y+4=0

a = 5; b = -270; c = +4;
Δ = b2-4ac
Δ = -2702-4·5·4
Δ = 72820
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:

$\sqrt{\Delta}=\sqrt{72820}=\sqrt{4*18205}=\sqrt{4}*\sqrt{18205}=2\sqrt{18205}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-2\sqrt{18205}}{2*5}=\frac{270-2\sqrt{18205}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+2\sqrt{18205}}{2*5}=\frac{270+2\sqrt{18205}}{10}
$