.75x(x+20)=2+.5(x-2)

Solution for .75x(x+20)=2+.5(x-2) equation:

.75x(x+20)=2+.5(x-2)

We move all terms to the left:

.75x(x+20)-(2+.5(x-2))=0

We multiply parentheses

x^2+20x-(2+.5(x-2))=0


We calculate terms in parentheses: -(2+.5(x-2)), so:

2+.5(x-2)

determiningTheFunctionDomain
.5(x-2)+2

We multiply parentheses

0.5x-1+2

We add all the numbers together, and all the variables

0.5x+1

Back to the equation:

-(0.5x+1)


We get rid of parentheses

x^2+20x-0.5x-1=0

We add all the numbers together, and all the variables

x^2+19.5x-1=0

a = 1; b = 19.5; c = -1;
Δ = b2-4ac
Δ = 19.52-4·1·(-1)
Δ = 384.25
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{-(19.5)-\sqrt{384.25}}{2*1}=\frac{-19.5-\sqrt{384.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19.5)+\sqrt{384.25}}{2*1}=\frac{-19.5+\sqrt{384.25}}{2}
$