x2+53x+592=0

Solution for x2+53x+592=0 equation:

x2+53x+592=0

We add all the numbers together, and all the variables

x^2+53x+592=0

a = 1; b = 53; c = +592;
Δ = b2-4ac
Δ = 532-4·1·592
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-21}{2*1}=\frac{-74}{2}
=-37
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+21}{2*1}=\frac{-32}{2}
=-16
$