X2+14x-169=0

Solution for X2+14x-169=0 equation:

X2+14X-169=0

We add all the numbers together, and all the variables

X^2+14X-169=0

a = 1; b = 14; c = -169;
Δ = b2-4ac
Δ = 142-4·1·(-169)
Δ = 872
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:

$\sqrt{\Delta}=\sqrt{872}=\sqrt{4*218}=\sqrt{4}*\sqrt{218}=2\sqrt{218}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{218}}{2*1}=\frac{-14-2\sqrt{218}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{218}}{2*1}=\frac{-14+2\sqrt{218}}{2}
$