y+1/2y=78

Solution for y+1/2y=78 equation:

y+1/2y=78

We move all terms to the left:

y+1/2y-(78)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We multiply all the terms by the denominator


y*2y-78*2y+1=0

Wy multiply elements

2y^2-156y+1=0

a = 2; b = -156; c = +1;
Δ = b2-4ac
Δ = -1562-4·2·1
Δ = 24328
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:

$\sqrt{\Delta}=\sqrt{24328}=\sqrt{4*6082}=\sqrt{4}*\sqrt{6082}=2\sqrt{6082}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-2\sqrt{6082}}{2*2}=\frac{156-2\sqrt{6082}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+2\sqrt{6082}}{2*2}=\frac{156+2\sqrt{6082}}{4}
$