x2+x=1/2

Solution for x2+x=1/2 equation:

x2+x=1/2

We move all terms to the left:

x2+x-(1/2)=0

We add all the numbers together, and all the variables

x2+x-(+1/2)=0

We add all the numbers together, and all the variables

x^2+x-(+1/2)=0

We get rid of parentheses

x^2+x-1/2=0

We multiply all the terms by the denominator


x^2*2+x*2-1=0

Wy multiply elements

2x^2+2x-1=0

a = 2; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·2·(-1)
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{3}}{2*2}=\frac{-2-2\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{3}}{2*2}=\frac{-2+2\sqrt{3}}{4}
$