x(18+4x)=10

Solution for x(18+4x)=10 equation:

x(18+4x)=10

We move all terms to the left:

x(18+4x)-(10)=0

We add all the numbers together, and all the variables

x(4x+18)-10=0

We multiply parentheses

4x^2+18x-10=0

a = 4; b = 18; c = -10;
Δ = b2-4ac
Δ = 182-4·4·(-10)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-22}{2*4}=\frac{-40}{8}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+22}{2*4}=\frac{4}{8}
=1/2
$