11x(x-1)=-9x^2+4

Solution for 11x(x-1)=-9x^2+4 equation:

11x(x-1)=-9x^2+4

We move all terms to the left:

11x(x-1)-(-9x^2+4)=0

We multiply parentheses

-(-9x^2+4)+11x^2-11x=0

We get rid of parentheses

9x^2+11x^2-11x-4=0

We add all the numbers together, and all the variables

20x^2-11x-4=0

a = 20; b = -11; c = -4;
Δ = b2-4ac
Δ = -112-4·20·(-4)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-21}{2*20}=\frac{-10}{40}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+21}{2*20}=\frac{32}{40}
=4/5
$