196=53x-x^2

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

196=53x-x^2

We move all terms to the left:

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

We get rid of parentheses

x^2-53x+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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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