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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((+4x^2-20x-16x+80))+x=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 add all the numbers together, and all the variables

x-(4x^2-36x+80)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-4x^2+37x-80=0

a = -4; b = 37; c = -80;
Δ = b2-4ac
Δ = 372-4·(-4)·(-80)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-\sqrt{89}}{2*-4}=\frac{-37-\sqrt{89}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{89}}{2*-4}=\frac{-37+\sqrt{89}}{-8}
$