y+4/7y=308

Solution for y+4/7y=308 equation:

y+4/7y=308

We move all terms to the left:

y+4/7y-(308)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R


We multiply all the terms by the denominator


y*7y-308*7y+4=0

Wy multiply elements

7y^2-2156y+4=0

a = 7; b = -2156; c = +4;
Δ = b2-4ac
Δ = -21562-4·7·4
Δ = 4648224
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:

$\sqrt{\Delta}=\sqrt{4648224}=\sqrt{16*290514}=\sqrt{16}*\sqrt{290514}=4\sqrt{290514}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2156)-4\sqrt{290514}}{2*7}=\frac{2156-4\sqrt{290514}}{14}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2156)+4\sqrt{290514}}{2*7}=\frac{2156+4\sqrt{290514}}{14}
$