6t^2-3t-5=3t^2+11t

Solution for 6t^2-3t-5=3t^2+11t equation:

6t^2-3t-5=3t^2+11t

We move all terms to the left:

6t^2-3t-5-(3t^2+11t)=0

We get rid of parentheses

6t^2-3t^2-3t-11t-5=0

We add all the numbers together, and all the variables

3t^2-14t-5=0

a = 3; b = -14; c = -5;
Δ = b2-4ac
Δ = -142-4·3·(-5)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-16}{2*3}=\frac{-2}{6}
=-1/3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+16}{2*3}=\frac{30}{6}
=5
$