6t(t+4)=5t-10

Solution for 6t(t+4)=5t-10 equation:

6t(t+4)=5t-10

We move all terms to the left:

6t(t+4)-(5t-10)=0

We multiply parentheses

6t^2+24t-(5t-10)=0

We get rid of parentheses

6t^2+24t-5t+10=0

We add all the numbers together, and all the variables

6t^2+19t+10=0

a = 6; b = 19; c = +10;
Δ = b2-4ac
Δ = 192-4·6·10
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*6}=\frac{-30}{12}
=-2+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+11}{2*6}=\frac{-8}{12}
=-2/3
$