24=(8-2x)(10-2x)

Solution for 24=(8-2x)(10-2x) equation:

24=(8-2x)(10-2x)

We move all terms to the left:

24-((8-2x)(10-2x))=0

We add all the numbers together, and all the variables

-((-2x+8)(-2x+10))+24=0

We multiply parentheses ..

-((+4x^2-20x-16x+80))+24=0


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

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-36x+80

Back to the equation:

-(4x^2-36x+80)


We get rid of parentheses

-4x^2+36x-80+24=0

We add all the numbers together, and all the variables

-4x^2+36x-56=0

a = -4; b = 36; c = -56;
Δ = b2-4ac
Δ = 362-4·(-4)·(-56)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-20}{2*-4}=\frac{-56}{-8}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+20}{2*-4}=\frac{-16}{-8}
=+2
$