5t^2-2t+8t=3

Solution for 5t^2-2t+8t=3 equation:

5t^2-2t+8t=3

We move all terms to the left:

5t^2-2t+8t-(3)=0

We add all the numbers together, and all the variables

5t^2+6t-3=0

a = 5; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·5·(-3)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{6}}{2*5}=\frac{-6-4\sqrt{6}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{6}}{2*5}=\frac{-6+4\sqrt{6}}{10}
$