1=(.08x)(1+.5x)

Solution for 1=(.08x)(1+.5x) equation:

1=(.08x)(1+.5x)

We move all terms to the left:

1-((.08x)(1+.5x))=0

We add all the numbers together, and all the variables

-((+.08x)(.5x+1))+1=0

We multiply parentheses ..

-((+x^2+x))+1=0


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

(+x^2+x)

We get rid of parentheses

x^2+x

Back to the equation:

-(x^2+x)


We get rid of parentheses

-x^2-x+1=0

We add all the numbers together, and all the variables

-1x^2-1x+1=0

a = -1; b = -1; c = +1;
Δ = b2-4ac
Δ = -12-4·(-1)·1
Δ = 5
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{-(-1)-\sqrt{5}}{2*-1}=\frac{1-\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{5}}{2*-1}=\frac{1+\sqrt{5}}{-2}
$