15t^2+30t=11t-6

Solution for 15t^2+30t=11t-6 equation:

15t^2+30t=11t-6

We move all terms to the left:

15t^2+30t-(11t-6)=0

We get rid of parentheses

15t^2+30t-11t+6=0

We add all the numbers together, and all the variables

15t^2+19t+6=0

a = 15; b = 19; c = +6;
Δ = b2-4ac
Δ = 192-4·15·6
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*15}=\frac{-20}{30}
=-2/3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+1}{2*15}=\frac{-18}{30}
=-3/5
$