6x(7x+9)+x^2*6=0

Solution for 6x(7x+9)+x^2*6=0 equation:

6x(7x+9)+x^2*6=0

We multiply parentheses

x^2*6+42x^2+54x=0

Wy multiply elements

6x^2+42x^2+54x=0

We add all the numbers together, and all the variables

48x^2+54x=0

a = 48; b = 54; c = 0;
Δ = b2-4ac
Δ = 542-4·48·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-54}{2*48}=\frac{-108}{96}
=-1+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+54}{2*48}=\frac{0}{96}
=0
$