X^2+26x+106=0

Solution for X^2+26x+106=0 equation:

X^2+26X+106=0

a = 1; b = 26; c = +106;
Δ = b2-4ac
Δ = 262-4·1·106
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-6\sqrt{7}}{2*1}=\frac{-26-6\sqrt{7}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+6\sqrt{7}}{2*1}=\frac{-26+6\sqrt{7}}{2}
$