5/7y+18=2y

Solution for 5/7y+18=2y equation:

5/7y+18=2y

We move all terms to the left:

5/7y+18-(2y)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R


We add all the numbers together, and all the variables

-2y+5/7y+18=0

We multiply all the terms by the denominator


-2y*7y+18*7y+5=0

Wy multiply elements

-14y^2+126y+5=0

a = -14; b = 126; c = +5;
Δ = b2-4ac
Δ = 1262-4·(-14)·5
Δ = 16156
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:

$\sqrt{\Delta}=\sqrt{16156}=\sqrt{4*4039}=\sqrt{4}*\sqrt{4039}=2\sqrt{4039}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-2\sqrt{4039}}{2*-14}=\frac{-126-2\sqrt{4039}}{-28}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+2\sqrt{4039}}{2*-14}=\frac{-126+2\sqrt{4039}}{-28}
$