X*(x-6)-4*(2+3x)=0

Solution for X*(x-6)-4*(2+3x)=0 equation:

X(X-6)-4(2+3X)=0

We add all the numbers together, and all the variables

X(X-6)-4(3X+2)=0

We multiply parentheses

X^2-6X-12X-8=0

We add all the numbers together, and all the variables

X^2-18X-8=0

a = 1; b = -18; c = -8;
Δ = b2-4ac
Δ = -182-4·1·(-8)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{89}}{2*1}=\frac{18-2\sqrt{89}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{89}}{2*1}=\frac{18+2\sqrt{89}}{2}
$