3t^2+2t-8=3

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

3t^2+2t-8=3

We move all terms to the left:

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

We add all the numbers together, and all the variables

3t^2+2t-11=0

a = 3; b = 2; c = -11;
Δ = b2-4ac
Δ = 22-4·3·(-11)
Δ = 136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{34}}{2*3}=\frac{-2-2\sqrt{34}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{34}}{2*3}=\frac{-2+2\sqrt{34}}{6}
$