3/5y+y=1800

Solution for 3/5y+y=1800 equation:

3/5y+y=1800

We move all terms to the left:

3/5y+y-(1800)=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-1800=0

We multiply all the terms by the denominator


y*5y-1800*5y+3=0

Wy multiply elements

5y^2-9000y+3=0

a = 5; b = -9000; c = +3;
Δ = b2-4ac
Δ = -90002-4·5·3
Δ = 80999940
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:

$\sqrt{\Delta}=\sqrt{80999940}=\sqrt{196*413265}=\sqrt{196}*\sqrt{413265}=14\sqrt{413265}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9000)-14\sqrt{413265}}{2*5}=\frac{9000-14\sqrt{413265}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9000)+14\sqrt{413265}}{2*5}=\frac{9000+14\sqrt{413265}}{10}
$