0.5x+x^2=0.75

Solution for 0.5x+x^2=0.75 equation:

0.5x+x^2=0.75

We move all terms to the left:

0.5x+x^2-(0.75)=0

We add all the numbers together, and all the variables

x^2+0.5x-0.75=0

a = 1; b = 0.5; c = -0.75;
Δ = b2-4ac
Δ = 0.52-4·1·(-0.75)
Δ = 3.25
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{-(0.5)-\sqrt{3.25}}{2*1}=\frac{-0.5-\sqrt{3.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{3.25}}{2*1}=\frac{-0.5+\sqrt{3.25}}{2}
$