X(X+1)+25x=1

Solution for X(X+1)+25x=1 equation:

X(X+1)+25X=1

We move all terms to the left:

X(X+1)+25X-(1)=0

We add all the numbers together, and all the variables

25X+X(X+1)-1=0

We multiply parentheses

X^2+25X+X-1=0

We add all the numbers together, and all the variables

X^2+26X-1=0

a = 1; b = 26; c = -1;
Δ = b2-4ac
Δ = 262-4·1·(-1)
Δ = 680
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:

$\sqrt{\Delta}=\sqrt{680}=\sqrt{4*170}=\sqrt{4}*\sqrt{170}=2\sqrt{170}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{170}}{2*1}=\frac{-26-2\sqrt{170}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{170}}{2*1}=\frac{-26+2\sqrt{170}}{2}
$