12s+12(s+5)=2s(s+5)

Solution for 12s+12(s+5)=2s(s+5) equation:

12s+12(s+5)=2s(s+5)

We move all terms to the left:

12s+12(s+5)-(2s(s+5))=0

We multiply parentheses

12s+12s-(2s(s+5))+60=0


We calculate terms in parentheses: -(2s(s+5)), so:

2s(s+5)

We multiply parentheses

2s^2+10s

Back to the equation:

-(2s^2+10s)


We add all the numbers together, and all the variables

24s-(2s^2+10s)+60=0

We get rid of parentheses

-2s^2+24s-10s+60=0

We add all the numbers together, and all the variables

-2s^2+14s+60=0

a = -2; b = 14; c = +60;
Δ = b2-4ac
Δ = 142-4·(-2)·60
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-26}{2*-2}=\frac{-40}{-4}
=+10
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+26}{2*-2}=\frac{12}{-4}
=-3
$