2s^2+10s-133=0

Solution for 2s^2+10s-133=0 equation:

2s^2+10s-133=0

a = 2; b = 10; c = -133;
Δ = b2-4ac
Δ = 102-4·2·(-133)
Δ = 1164
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:

$\sqrt{\Delta}=\sqrt{1164}=\sqrt{4*291}=\sqrt{4}*\sqrt{291}=2\sqrt{291}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{291}}{2*2}=\frac{-10-2\sqrt{291}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{291}}{2*2}=\frac{-10+2\sqrt{291}}{4}
$