x(x-4)=4x+3x+6

Solution for x(x-4)=4x+3x+6 equation:

x(x-4)=4x+3x+6

We move all terms to the left:

x(x-4)-(4x+3x+6)=0

We add all the numbers together, and all the variables

x(x-4)-(7x+6)=0

We multiply parentheses

x^2-4x-(7x+6)=0

We get rid of parentheses

x^2-4x-7x-6=0

We add all the numbers together, and all the variables

x^2-11x-6=0

a = 1; b = -11; c = -6;
Δ = b2-4ac
Δ = -112-4·1·(-6)
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{145}}{2*1}=\frac{11-\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{145}}{2*1}=\frac{11+\sqrt{145}}{2}
$