3t^2+4t+8=-6t

Solution for 3t^2+4t+8=-6t equation:

3t^2+4t+8=-6t

We move all terms to the left:

3t^2+4t+8-(-6t)=0

We get rid of parentheses

3t^2+4t+6t+8=0

We add all the numbers together, and all the variables

3t^2+10t+8=0

a = 3; b = 10; c = +8;
Δ = b2-4ac
Δ = 102-4·3·8
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2}{2*3}=\frac{-12}{6}
=-2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2}{2*3}=\frac{-8}{6}
=-1+1/3
$