6x(4x+1)-5x^2=4x

Solution for 6x(4x+1)-5x^2=4x equation:

6x(4x+1)-5x^2=4x

We move all terms to the left:

6x(4x+1)-5x^2-(4x)=0

We add all the numbers together, and all the variables

-5x^2-4x+6x(4x+1)=0

We multiply parentheses

-5x^2+24x^2-4x+6x=0

We add all the numbers together, and all the variables

19x^2+2x=0

a = 19; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·19·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*19}=\frac{-4}{38}
=-2/19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*19}=\frac{0}{38}
=0
$