4x(-2-x)=13+5(x-3)

Solution for 4x(-2-x)=13+5(x-3) equation:

4x(-2-x)=13+5(x-3)

We move all terms to the left:

4x(-2-x)-(13+5(x-3))=0

We add all the numbers together, and all the variables

4x(-1x-2)-(13+5(x-3))=0

We multiply parentheses

-4x^2-8x-(13+5(x-3))=0


We calculate terms in parentheses: -(13+5(x-3)), so:

13+5(x-3)

determiningTheFunctionDomain
5(x-3)+13

We multiply parentheses

5x-15+13

We add all the numbers together, and all the variables

5x-2

Back to the equation:

-(5x-2)


We get rid of parentheses

-4x^2-8x-5x+2=0

We add all the numbers together, and all the variables

-4x^2-13x+2=0

a = -4; b = -13; c = +2;
Δ = b2-4ac
Δ = -132-4·(-4)·2
Δ = 201
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{-(-13)-\sqrt{201}}{2*-4}=\frac{13-\sqrt{201}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{201}}{2*-4}=\frac{13+\sqrt{201}}{-8}
$