0=-y^2+49+2y^2-21y+55

Solution for 0=-y^2+49+2y^2-21y+55 equation:

0=-y^2+49+2y^2-21y+55

We move all terms to the left:

0-(-y^2+49+2y^2-21y+55)=0

We add all the numbers together, and all the variables

-(-y^2+49+2y^2-21y+55)=0

We get rid of parentheses

y^2-2y^2+21y-49-55=0

We add all the numbers together, and all the variables

-1y^2+21y-104=0

a = -1; b = 21; c = -104;
Δ = b2-4ac
Δ = 212-4·(-1)·(-104)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-5}{2*-1}=\frac{-26}{-2}
=+13
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+5}{2*-1}=\frac{-16}{-2}
=+8
$