(3s+5)(5s+8=0)

Solution for (3s+5)(5s+8=0) equation:

(3s+5)(5s+8=0)

We move all terms to the left:

(3s+5)(5s+8-(0))=0

We add all the numbers together, and all the variables

(3s+5)(5s+8)=0

We multiply parentheses ..

(+15s^2+24s+25s+40)=0

We get rid of parentheses

15s^2+24s+25s+40=0

We add all the numbers together, and all the variables

15s^2+49s+40=0

a = 15; b = 49; c = +40;
Δ = b2-4ac
Δ = 492-4·15·40
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-1}{2*15}=\frac{-50}{30}
=-1+2/3
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+1}{2*15}=\frac{-48}{30}
=-1+3/5
$