3x-2.5x^2=-1

Solution for 3x-2.5x^2=-1 equation:

3x-2.5x^2=-1

We move all terms to the left:

3x-2.5x^2-(-1)=0

We add all the numbers together, and all the variables

-2.5x^2+3x+1=0

a = -2.5; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-2.5)·1
Δ = 19
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{19}}{2*-2.5}=\frac{-3-\sqrt{19}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{19}}{2*-2.5}=\frac{-3+\sqrt{19}}{-5}
$