x^2+14x-53=0

Solution for x^2+14x-53=0 equation:

x^2+14x-53=0

a = 1; b = 14; c = -53;
Δ = b2-4ac
Δ = 142-4·1·(-53)
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{102}}{2*1}=\frac{-14-2\sqrt{102}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{102}}{2*1}=\frac{-14+2\sqrt{102}}{2}
$