11x^2+x+6=6+4x^2

Solution for 11x^2+x+6=6+4x^2 equation:

11x^2+x+6=6+4x^2

We move all terms to the left:

11x^2+x+6-(6+4x^2)=0

We get rid of parentheses

11x^2-4x^2+x-6+6=0

We add all the numbers together, and all the variables

7x^2+x=0

a = 7; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·7·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*7}=\frac{-2}{14}
=-1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*7}=\frac{0}{14}
=0
$