s^2+2s-33=0

Solution for s^2+2s-33=0 equation:

s^2+2s-33=0

a = 1; b = 2; c = -33;
Δ = b2-4ac
Δ = 22-4·1·(-33)
Δ = 136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{34}}{2*1}=\frac{-2-2\sqrt{34}}{2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{34}}{2*1}=\frac{-2+2\sqrt{34}}{2}
$