2.5t^2-2t=3

Solution for 2.5t^2-2t=3 equation:

2.5t^2-2t=3

We move all terms to the left:

2.5t^2-2t-(3)=0

a = 2.5; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·2.5·(-3)
Δ = 34
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-\sqrt{34}}{2*2.5}=\frac{2-\sqrt{34}}{5}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{34}}{2*2.5}=\frac{2+\sqrt{34}}{5}
$