-4x(4x-9)=2x

Solution for -4x(4x-9)=2x equation:

-4x(4x-9)=2x

We move all terms to the left:

-4x(4x-9)-(2x)=0

We add all the numbers together, and all the variables

-2x-4x(4x-9)=0

We multiply parentheses

-16x^2-2x+36x=0

We add all the numbers together, and all the variables

-16x^2+34x=0

a = -16; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·(-16)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*-16}=\frac{-68}{-32}
=2+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*-16}=\frac{0}{-32}
=0
$