x(4x+25)=x+8

Solution for x(4x+25)=x+8 equation:

x(4x+25)=x+8

We move all terms to the left:

x(4x+25)-(x+8)=0

We multiply parentheses

4x^2+25x-(x+8)=0

We get rid of parentheses

4x^2+25x-x-8=0

We add all the numbers together, and all the variables

4x^2+24x-8=0

a = 4; b = 24; c = -8;
Δ = b2-4ac
Δ = 242-4·4·(-8)
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{11}}{2*4}=\frac{-24-8\sqrt{11}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{11}}{2*4}=\frac{-24+8\sqrt{11}}{8}
$