53x*(53-x)=2330

Solution for 53x*(53-x)=2330 equation:

53x(53-x)=2330

We move all terms to the left:

53x(53-x)-(2330)=0

We add all the numbers together, and all the variables

53x(-1x+53)-2330=0

We multiply parentheses

-53x^2+2809x-2330=0

a = -53; b = 2809; c = -2330;
Δ = b2-4ac
Δ = 28092-4·(-53)·(-2330)
Δ = 7396521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2809)-\sqrt{7396521}}{2*-53}=\frac{-2809-\sqrt{7396521}}{-106}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2809)+\sqrt{7396521}}{2*-53}=\frac{-2809+\sqrt{7396521}}{-106}
$