2t^2-8t=-3

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

2t^2-8t=-3

We move all terms to the left:

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

We add all the numbers together, and all the variables

2t^2-8t+3=0

a = 2; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·2·3
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{10}}{2*2}=\frac{8-2\sqrt{10}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{10}}{2*2}=\frac{8+2\sqrt{10}}{4}
$