5/3*y-y=1660

Solution for 5/3*y-y=1660 equation:

5/3y-y=1660

We move all terms to the left:

5/3y-y-(1660)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

-1y+5/3y-1660=0

We multiply all the terms by the denominator


-1y*3y-1660*3y+5=0

Wy multiply elements

-3y^2-4980y+5=0

a = -3; b = -4980; c = +5;
Δ = b2-4ac
Δ = -49802-4·(-3)·5
Δ = 24800460
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:

$\sqrt{\Delta}=\sqrt{24800460}=\sqrt{4*6200115}=\sqrt{4}*\sqrt{6200115}=2\sqrt{6200115}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4980)-2\sqrt{6200115}}{2*-3}=\frac{4980-2\sqrt{6200115}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4980)+2\sqrt{6200115}}{2*-3}=\frac{4980+2\sqrt{6200115}}{-6}
$