x^2-53x-196=0

Solution for x^2-53x-196=0 equation:

x^2-53x-196=0

a = 1; b = -53; c = -196;
Δ = b2-4ac
Δ = -532-4·1·(-196)
Δ = 3593
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{-(-53)-\sqrt{3593}}{2*1}=\frac{53-\sqrt{3593}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+\sqrt{3593}}{2*1}=\frac{53+\sqrt{3593}}{2}
$