-2x(x+1/3)+9x=4

Solution for -2x(x+1/3)+9x=4 equation:

-2x(x+1/3)+9x=4

We move all terms to the left:

-2x(x+1/3)+9x-(4)=0

We add all the numbers together, and all the variables

-2x(+x+1/3)+9x-4=0

We add all the numbers together, and all the variables

9x-2x(+x+1/3)-4=0

We multiply parentheses

-2x^2-2x^2+9x-4=0

We add all the numbers together, and all the variables

-4x^2+9x-4=0

a = -4; b = 9; c = -4;
Δ = b2-4ac
Δ = 92-4·(-4)·(-4)
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{17}}{2*-4}=\frac{-9-\sqrt{17}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{17}}{2*-4}=\frac{-9+\sqrt{17}}{-8}
$