40=(1/2)*(96-x)

Solution for 40=(1/2)*(96-x) equation:

40=(1/2)(96-x)

We move all terms to the left:

40-((1/2)(96-x))=0


Domain of the equation: 2)(96-x))!=0

x∈R


We add all the numbers together, and all the variables

-((+1/2)(-1x+96))+40=0

We multiply parentheses ..

-((-1x^2+1/2*96))+40=0

We multiply all the terms by the denominator


-((-1x^2+1+40*2*96))=0


We calculate terms in parentheses: -((-1x^2+1+40*2*96)), so:

(-1x^2+1+40*2*96)

We get rid of parentheses

-1x^2+1+40*2*96

We add all the numbers together, and all the variables

-1x^2+7681

Back to the equation:

-(-1x^2+7681)


We get rid of parentheses

1x^2-7681=0

We add all the numbers together, and all the variables

x^2-7681=0

a = 1; b = 0; c = -7681;
Δ = b2-4ac
Δ = 02-4·1·(-7681)
Δ = 30724
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:

$\sqrt{\Delta}=\sqrt{30724}=\sqrt{4*7681}=\sqrt{4}*\sqrt{7681}=2\sqrt{7681}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{7681}}{2*1}=\frac{0-2\sqrt{7681}}{2}
=-\frac{2\sqrt{7681}}{2}
=-\sqrt{7681}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{7681}}{2*1}=\frac{0+2\sqrt{7681}}{2}
=\frac{2\sqrt{7681}}{2}
=\sqrt{7681}
$