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

Solution for 6x^2-11x^2-6x=0 equation:

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

We add all the numbers together, and all the variables

-5x^2-6x=0

a = -5; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-5)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-5}=\frac{0}{-10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-5}=\frac{12}{-10}
=-1+1/5
$