X=(x1+x2)/2

Solution for X=(x1+x2)/2 equation:

X=(X1+X2)/2

We move all terms to the left:

X-((X1+X2)/2)=0

We add all the numbers together, and all the variables

-((+X+X^2)/2)+X=0

We multiply all the terms by the denominator


-((+X+X^2)+X*2)=0


We calculate terms in parentheses: -((+X+X^2)+X*2), so:

(+X+X^2)+X*2

Wy multiply elements

(+X+X^2)+2X

We get rid of parentheses

X^2+X+2X

We add all the numbers together, and all the variables

X^2+3X

Back to the equation:

-(X^2+3X)


We get rid of parentheses

-X^2-3X=0

We add all the numbers together, and all the variables

-1X^2-3X=0

a = -1; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-1)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-1}=\frac{0}{-2}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-1}=\frac{6}{-2}
=-3
$