4x+29=5-8x(x+6)

Solution for 4x+29=5-8x(x+6) equation:

4x+29=5-8x(x+6)

We move all terms to the left:

4x+29-(5-8x(x+6))=0


We calculate terms in parentheses: -(5-8x(x+6)), so:

5-8x(x+6)

determiningTheFunctionDomain
-8x(x+6)+5

We multiply parentheses

-8x^2-48x+5

Back to the equation:

-(-8x^2-48x+5)


We get rid of parentheses

8x^2+48x+4x-5+29=0

We add all the numbers together, and all the variables

8x^2+52x+24=0

a = 8; b = 52; c = +24;
Δ = b2-4ac
Δ = 522-4·8·24
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-44}{2*8}=\frac{-96}{16}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+44}{2*8}=\frac{-8}{16}
=-1/2
$