12t(t+2)=5t-5

Solution for 12t(t+2)=5t-5 equation:

12t(t+2)=5t-5

We move all terms to the left:

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

We multiply parentheses

12t^2+24t-(5t-5)=0

We get rid of parentheses

12t^2+24t-5t+5=0

We add all the numbers together, and all the variables

12t^2+19t+5=0

a = 12; b = 19; c = +5;
Δ = b2-4ac
Δ = 192-4·12·5
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-11}{2*12}=\frac{-30}{24}
=-1+1/4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+11}{2*12}=\frac{-8}{24}
=-1/3
$