(s+5)(2s+3)=204

Solution for (s+5)(2s+3)=204 equation:

(s+5)(2s+3)=204

We move all terms to the left:

(s+5)(2s+3)-(204)=0

We multiply parentheses ..

(+2s^2+3s+10s+15)-204=0

We get rid of parentheses

2s^2+3s+10s+15-204=0

We add all the numbers together, and all the variables

2s^2+13s-189=0

a = 2; b = 13; c = -189;
Δ = b2-4ac
Δ = 132-4·2·(-189)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-41}{2*2}=\frac{-54}{4}
=-13+1/2
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+41}{2*2}=\frac{28}{4}
=7
$