1/5y+y+90=360

Solution for 1/5y+y+90=360 equation:

1/5y+y+90=360

We move all terms to the left:

1/5y+y+90-(360)=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+1/5y-270=0

We multiply all the terms by the denominator


y*5y-270*5y+1=0

Wy multiply elements

5y^2-1350y+1=0

a = 5; b = -1350; c = +1;
Δ = b2-4ac
Δ = -13502-4·5·1
Δ = 1822480
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:

$\sqrt{\Delta}=\sqrt{1822480}=\sqrt{16*113905}=\sqrt{16}*\sqrt{113905}=4\sqrt{113905}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1350)-4\sqrt{113905}}{2*5}=\frac{1350-4\sqrt{113905}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1350)+4\sqrt{113905}}{2*5}=\frac{1350+4\sqrt{113905}}{10}
$