x^2+58x+14=0

Solution for x^2+58x+14=0 equation:

x^2+58x+14=0

a = 1; b = 58; c = +14;
Δ = b2-4ac
Δ = 582-4·1·14
Δ = 3308
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3308}=\sqrt{4*827}=\sqrt{4}*\sqrt{827}=2\sqrt{827}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-2\sqrt{827}}{2*1}=\frac{-58-2\sqrt{827}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+2\sqrt{827}}{2*1}=\frac{-58+2\sqrt{827}}{2}
$