53y-y^2=196

Solution for 53y-y^2=196 equation:

53y-y^2=196

We move all terms to the left:

53y-y^2-(196)=0

We add all the numbers together, and all the variables

-1y^2+53y-196=0

a = -1; b = 53; c = -196;
Δ = b2-4ac
Δ = 532-4·(-1)·(-196)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-45}{2*-1}=\frac{-98}{-2}
=+49
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+45}{2*-1}=\frac{-8}{-2}
=+4
$