w2+26w+21=0

Solution for w2+26w+21=0 equation:

w2+26w+21=0

We add all the numbers together, and all the variables

w^2+26w+21=0

a = 1; b = 26; c = +21;
Δ = b2-4ac
Δ = 262-4·1·21
Δ = 592
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-4\sqrt{37}}{2*1}=\frac{-26-4\sqrt{37}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+4\sqrt{37}}{2*1}=\frac{-26+4\sqrt{37}}{2}
$