x^2+14x+x^2=289

Solution for x^2+14x+x^2=289 equation:

x^2+14x+x^2=289

We move all terms to the left:

x^2+14x+x^2-(289)=0

We add all the numbers together, and all the variables

2x^2+14x-289=0

a = 2; b = 14; c = -289;
Δ = b2-4ac
Δ = 142-4·2·(-289)
Δ = 2508
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:

$\sqrt{\Delta}=\sqrt{2508}=\sqrt{4*627}=\sqrt{4}*\sqrt{627}=2\sqrt{627}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{627}}{2*2}=\frac{-14-2\sqrt{627}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{627}}{2*2}=\frac{-14+2\sqrt{627}}{4}
$