1/5y-y=76

Solution for 1/5y-y=76 equation:

1/5y-y=76

We move all terms to the left:

1/5y-y-(76)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

-1y+1/5y-76=0

We multiply all the terms by the denominator


-1y*5y-76*5y+1=0

Wy multiply elements

-5y^2-380y+1=0

a = -5; b = -380; c = +1;
Δ = b2-4ac
Δ = -3802-4·(-5)·1
Δ = 144420
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:

$\sqrt{\Delta}=\sqrt{144420}=\sqrt{4*36105}=\sqrt{4}*\sqrt{36105}=2\sqrt{36105}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-380)-2\sqrt{36105}}{2*-5}=\frac{380-2\sqrt{36105}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-380)+2\sqrt{36105}}{2*-5}=\frac{380+2\sqrt{36105}}{-10}
$