24-5x=4-8x(x+5)

Solution for 24-5x=4-8x(x+5) equation:

24-5x=4-8x(x+5)

We move all terms to the left:

24-5x-(4-8x(x+5))=0


We calculate terms in parentheses: -(4-8x(x+5)), so:

4-8x(x+5)

determiningTheFunctionDomain
-8x(x+5)+4

We multiply parentheses

-8x^2-40x+4

Back to the equation:

-(-8x^2-40x+4)


We get rid of parentheses

8x^2+40x-5x-4+24=0

We add all the numbers together, and all the variables

8x^2+35x+20=0

a = 8; b = 35; c = +20;
Δ = b2-4ac
Δ = 352-4·8·20
Δ = 585
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-3\sqrt{65}}{2*8}=\frac{-35-3\sqrt{65}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+3\sqrt{65}}{2*8}=\frac{-35+3\sqrt{65}}{16}
$