6t(t+4)=5t-15

Solution for 6t(t+4)=5t-15 equation:

6t(t+4)=5t-15

We move all terms to the left:

6t(t+4)-(5t-15)=0

We multiply parentheses

6t^2+24t-(5t-15)=0

We get rid of parentheses

6t^2+24t-5t+15=0

We add all the numbers together, and all the variables

6t^2+19t+15=0

a = 6; b = 19; c = +15;
Δ = b2-4ac
Δ = 192-4·6·15
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-1}{2*6}=\frac{-20}{12}
=-1+2/3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+1}{2*6}=\frac{-18}{12}
=-1+1/2
$