0.5x^2+x=2

Solution for 0.5x^2+x=2 equation:

0.5x^2+x=2

We move all terms to the left:

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}
$