676-x^2-26x=0

Solution for 676-x^2-26x=0 equation:

676-x^2-26x=0

We add all the numbers together, and all the variables

-1x^2-26x+676=0

a = -1; b = -26; c = +676;
Δ = b2-4ac
Δ = -262-4·(-1)·676
Δ = 3380
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:

$\sqrt{\Delta}=\sqrt{3380}=\sqrt{676*5}=\sqrt{676}*\sqrt{5}=26\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-26\sqrt{5}}{2*-1}=\frac{26-26\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+26\sqrt{5}}{2*-1}=\frac{26+26\sqrt{5}}{-2}
$