4-x=(x+8)(2x+13)

Solution for 4-x=(x+8)(2x+13) equation:

4-x=(x+8)(2x+13)

We move all terms to the left:

4-x-((x+8)(2x+13))=0

We add all the numbers together, and all the variables

-1x-((x+8)(2x+13))+4=0

We multiply parentheses ..

-((+2x^2+13x+16x+104))-1x+4=0


We calculate terms in parentheses: -((+2x^2+13x+16x+104)), so:

(+2x^2+13x+16x+104)

We get rid of parentheses

2x^2+13x+16x+104

We add all the numbers together, and all the variables

2x^2+29x+104

Back to the equation:

-(2x^2+29x+104)


We add all the numbers together, and all the variables

-1x-(2x^2+29x+104)+4=0

We get rid of parentheses

-2x^2-1x-29x-104+4=0

We add all the numbers together, and all the variables

-2x^2-30x-100=0

a = -2; b = -30; c = -100;
Δ = b2-4ac
Δ = -302-4·(-2)·(-100)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10}{2*-2}=\frac{20}{-4}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10}{2*-2}=\frac{40}{-4}
=-10
$