w*w+26*w-153=0

Solution for w*w+26*w-153=0 equation:

w*w+26w-153=0

We add all the numbers together, and all the variables

26w+w*w-153=0

Wy multiply elements

w^2+26w-153=0

a = 1; b = 26; c = -153;
Δ = b2-4ac
Δ = 262-4·1·(-153)
Δ = 1288
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:

$\sqrt{\Delta}=\sqrt{1288}=\sqrt{4*322}=\sqrt{4}*\sqrt{322}=2\sqrt{322}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{322}}{2*1}=\frac{-26-2\sqrt{322}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{322}}{2*1}=\frac{-26+2\sqrt{322}}{2}
$