3/5y+y=180

Solution for 3/5y+y=180 equation:

3/5y+y=180

We move all terms to the left:

3/5y+y-(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+3/5y-180=0

We multiply all the terms by the denominator


y*5y-180*5y+3=0

Wy multiply elements

5y^2-900y+3=0

a = 5; b = -900; c = +3;
Δ = b2-4ac
Δ = -9002-4·5·3
Δ = 809940
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:

$\sqrt{\Delta}=\sqrt{809940}=\sqrt{4*202485}=\sqrt{4}*\sqrt{202485}=2\sqrt{202485}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-2\sqrt{202485}}{2*5}=\frac{900-2\sqrt{202485}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+2\sqrt{202485}}{2*5}=\frac{900+2\sqrt{202485}}{10}
$