-2t^2+3t=1

Solution for -2t^2+3t=1 equation:

-2t^2+3t=1

We move all terms to the left:

-2t^2+3t-(1)=0

a = -2; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·(-2)·(-1)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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