20=(x+3)((1/2)x)

Solution for 20=(x+3)((1/2)x) equation:

20=(x+3)((1/2)x)

We move all terms to the left:

20-((x+3)((1/2)x))=0


Domain of the equation: 2)x))!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-((x+3)((+1/2)x))+20=0

We multiply all the terms by the denominator


-((x+3)((+1+20*2)x))=0


We calculate terms in parentheses: -((x+3)((+1+20*2)x)), so:

(x+3)((+1+20*2)x)

We add all the numbers together, and all the variables

(x+3)(41x)

We add all the numbers together, and all the variables

(x+3)41x

We multiply parentheses

41x^2+123x

Back to the equation:

-(41x^2+123x)


We get rid of parentheses

-41x^2-123x=0

a = -41; b = -123; c = 0;
Δ = b2-4ac
Δ = -1232-4·(-41)·0
Δ = 15129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15129}=123$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-123)-123}{2*-41}=\frac{0}{-82}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-123)+123}{2*-41}=\frac{246}{-82}
=-3
$