38.75=80-(10-2x)(8-2x)

Solution for 38.75=80-(10-2x)(8-2x) equation:

38.75=80-(10-2x)(8-2x)

We move all terms to the left:

38.75-(80-(10-2x)(8-2x))=0

We add all the numbers together, and all the variables

-(80-(-2x+10)(-2x+8))+38.75=0

We multiply parentheses ..

-(80-(+4x^2-16x-20x+80))+38.75=0


We calculate terms in parentheses: -(80-(+4x^2-16x-20x+80)), so:

80-(+4x^2-16x-20x+80)

determiningTheFunctionDomain
-(+4x^2-16x-20x+80)+80

We get rid of parentheses

-4x^2+16x+20x-80+80

We add all the numbers together, and all the variables

-4x^2+36x

Back to the equation:

-(-4x^2+36x)


We get rid of parentheses

4x^2-36x+38.75=0

a = 4; b = -36; c = +38.75;
Δ = b2-4ac
Δ = -362-4·4·38.75
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-26}{2*4}=\frac{10}{8}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+26}{2*4}=\frac{62}{8}
=7+3/4
$