2*(y^-14y+49)-y*(2y-14)=0

Solution for 2*(y^-14y+49)-y*(2y-14)=0 equation:

2(y^-14y+49)-y(2y-14)=0

We multiply parentheses

-2y^2+2y-28y+14y+98=0

We add all the numbers together, and all the variables

-2y^2-12y+98=0

a = -2; b = -12; c = +98;
Δ = b2-4ac
Δ = -122-4·(-2)·98
Δ = 928
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:

$\sqrt{\Delta}=\sqrt{928}=\sqrt{16*58}=\sqrt{16}*\sqrt{58}=4\sqrt{58}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{58}}{2*-2}=\frac{12-4\sqrt{58}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{58}}{2*-2}=\frac{12+4\sqrt{58}}{-4}
$