s^2-7s-16=-32+5

Solution for s^2-7s-16=-32+5 equation:

s^2-7s-16=-32+5

We move all terms to the left:

s^2-7s-16-(-32+5)=0

We add all the numbers together, and all the variables

s^2-7s-16-(-27)=0

We add all the numbers together, and all the variables

s^2-7s+11=0

a = 1; b = -7; c = +11;
Δ = b2-4ac
Δ = -72-4·1·11
Δ = 5
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{5}}{2*1}=\frac{7-\sqrt{5}}{2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{5}}{2*1}=\frac{7+\sqrt{5}}{2}
$