X^2+196x=26^2

Solution for X^2+196x=26^2 equation:

X^2+196X=26^2

We move all terms to the left:

X^2+196X-(26^2)=0

We add all the numbers together, and all the variables

X^2+196X-676=0

a = 1; b = 196; c = -676;
Δ = b2-4ac
Δ = 1962-4·1·(-676)
Δ = 41120
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:

$\sqrt{\Delta}=\sqrt{41120}=\sqrt{16*2570}=\sqrt{16}*\sqrt{2570}=4\sqrt{2570}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(196)-4\sqrt{2570}}{2*1}=\frac{-196-4\sqrt{2570}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(196)+4\sqrt{2570}}{2*1}=\frac{-196+4\sqrt{2570}}{2}
$