(X+1)(X+2)(4)=24x+1

Solution for (X+1)(X+2)(4)=24x+1 equation:

(X+1)(X+2)(4)=24X+1

We move all terms to the left:

(X+1)(X+2)(4)-(24X+1)=0

We get rid of parentheses

(X+1)(X+2)4-24X-1=0

We multiply parentheses ..

(+X^2+2X+X+2)4-24X-1=0

We multiply parentheses

4X^2+8X+4X-24X+8-1=0

We add all the numbers together, and all the variables

4X^2-12X+7=0

a = 4; b = -12; c = +7;
Δ = b2-4ac
Δ = -122-4·4·7
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{2}}{2*4}=\frac{12-4\sqrt{2}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{2}}{2*4}=\frac{12+4\sqrt{2}}{8}
$