x(4x+18)=166

Solution for x(4x+18)=166 equation:

x(4x+18)=166

We move all terms to the left:

x(4x+18)-(166)=0

We multiply parentheses

4x^2+18x-166=0

a = 4; b = 18; c = -166;
Δ = b2-4ac
Δ = 182-4·4·(-166)
Δ = 2980
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:

$\sqrt{\Delta}=\sqrt{2980}=\sqrt{4*745}=\sqrt{4}*\sqrt{745}=2\sqrt{745}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{745}}{2*4}=\frac{-18-2\sqrt{745}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{745}}{2*4}=\frac{-18+2\sqrt{745}}{8}
$