x(2+5x)=32

Solution for x(2+5x)=32 equation:

x(2+5x)=32

We move all terms to the left:

x(2+5x)-(32)=0

We add all the numbers together, and all the variables

x(5x+2)-32=0

We multiply parentheses

5x^2+2x-32=0

a = 5; b = 2; c = -32;
Δ = b2-4ac
Δ = 22-4·5·(-32)
Δ = 644
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:

$\sqrt{\Delta}=\sqrt{644}=\sqrt{4*161}=\sqrt{4}*\sqrt{161}=2\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{161}}{2*5}=\frac{-2-2\sqrt{161}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{161}}{2*5}=\frac{-2+2\sqrt{161}}{10}
$