-0.5x^2+2.5x+1=1.5x

Solution for -0.5x^2+2.5x+1=1.5x equation:

-0.5x^2+2.5x+1=1.5x

We move all terms to the left:

-0.5x^2+2.5x+1-(1.5x)=0

We add all the numbers together, and all the variables

-0.5x^2+2.5x-(+1.5x)+1=0

We get rid of parentheses

-0.5x^2+2.5x-1.5x+1=0

We add all the numbers together, and all the variables

-0.5x^2+x+1=0

a = -0.5; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-0.5)·1
Δ = 3
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{-(1)-\sqrt{3}}{2*-0.5}=\frac{-1-\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{3}}{2*-0.5}=\frac{-1+\sqrt{3}}{-1}
$