12s+12(s+10)=s(s+10)

Solution for 12s+12(s+10)=s(s+10) equation:

12s+12(s+10)=s(s+10)

We move all terms to the left:

12s+12(s+10)-(s(s+10))=0

We multiply parentheses

12s+12s-(s(s+10))+120=0


We calculate terms in parentheses: -(s(s+10)), so:

s(s+10)

We multiply parentheses

s^2+10s

Back to the equation:

-(s^2+10s)


We add all the numbers together, and all the variables

24s-(s^2+10s)+120=0

We get rid of parentheses

-s^2+24s-10s+120=0

We add all the numbers together, and all the variables

-1s^2+14s+120=0

a = -1; b = 14; c = +120;
Δ = b2-4ac
Δ = 142-4·(-1)·120
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*-1}=\frac{-40}{-2}
=+20
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+26}{2*-1}=\frac{12}{-2}
=-6
$