x2+26x=33

Solution for x2+26x=33 equation:

x2+26x=33

We move all terms to the left:

x2+26x-(33)=0

We add all the numbers together, and all the variables

x^2+26x-33=0

a = 1; b = 26; c = -33;
Δ = b2-4ac
Δ = 262-4·1·(-33)
Δ = 808
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:

$\sqrt{\Delta}=\sqrt{808}=\sqrt{4*202}=\sqrt{4}*\sqrt{202}=2\sqrt{202}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{202}}{2*1}=\frac{-26-2\sqrt{202}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{202}}{2*1}=\frac{-26+2\sqrt{202}}{2}
$