X^2-2x=0.5x+1.5

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

X^2-2X=0.5X+1.5

We move all terms to the left:

X^2-2X-(0.5X+1.5)=0

We get rid of parentheses

X^2-2X-0.5X-1.5=0

We add all the numbers together, and all the variables

X^2-2.5X-1.5=0

a = 1; b = -2.5; c = -1.5;
Δ = b2-4ac
Δ = -2.52-4·1·(-1.5)
Δ = 12.25
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{-(-2.5)-\sqrt{12.25}}{2*1}=\frac{2.5-\sqrt{12.25}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.5)+\sqrt{12.25}}{2*1}=\frac{2.5+\sqrt{12.25}}{2}
$