x+3=1+0.5x2

Solution for x+3=1+0.5x2 equation:

x+3=1+0.5x^2

We move all terms to the left:

x+3-(1+0.5x^2)=0

We get rid of parentheses

-0.5x^2+x-1+3=0

We add all the numbers together, and all the variables

-0.5x^2+x+2=0

a = -0.5; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-0.5)·2
Δ = 5
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{5}}{2*-0.5}=\frac{-1-\sqrt{5}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{5}}{2*-0.5}=\frac{-1+\sqrt{5}}{-1}
$