53x-x^2=702

Solution for 53x-x^2=702 equation:

53x-x^2=702

We move all terms to the left:

53x-x^2-(702)=0

We add all the numbers together, and all the variables

-1x^2+53x-702=0

a = -1; b = 53; c = -702;
Δ = b2-4ac
Δ = 532-4·(-1)·(-702)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-1}{2*-1}=\frac{-54}{-2}
=+27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+1}{2*-1}=\frac{-52}{-2}
=+26
$