x2+(x-7)2=3809

Solution for x2+(x-7)2=3809 equation:

x2+(x-7)2=3809

We move all terms to the left:

x2+(x-7)2-(3809)=0

We add all the numbers together, and all the variables

x^2+(x-7)2-3809=0

We multiply parentheses

x^2+2x-14-3809=0

We add all the numbers together, and all the variables

x^2+2x-3823=0

a = 1; b = 2; c = -3823;
Δ = b2-4ac
Δ = 22-4·1·(-3823)
Δ = 15296
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:

$\sqrt{\Delta}=\sqrt{15296}=\sqrt{64*239}=\sqrt{64}*\sqrt{239}=8\sqrt{239}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-8\sqrt{239}}{2*1}=\frac{-2-8\sqrt{239}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8\sqrt{239}}{2*1}=\frac{-2+8\sqrt{239}}{2}
$