1/3y-y=76

Solution for 1/3y-y=76 equation:

1/3y-y=76

We move all terms to the left:

1/3y-y-(76)=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+1/3y-76=0

We multiply all the terms by the denominator


-1y*3y-76*3y+1=0

Wy multiply elements

-3y^2-228y+1=0

a = -3; b = -228; c = +1;
Δ = b2-4ac
Δ = -2282-4·(-3)·1
Δ = 51996
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:

$\sqrt{\Delta}=\sqrt{51996}=\sqrt{4*12999}=\sqrt{4}*\sqrt{12999}=2\sqrt{12999}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-228)-2\sqrt{12999}}{2*-3}=\frac{228-2\sqrt{12999}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-228)+2\sqrt{12999}}{2*-3}=\frac{228+2\sqrt{12999}}{-6}
$