x=-9x^2-5x+3

Solution for x=-9x^2-5x+3 equation:

x=-9x^2-5x+3

We move all terms to the left:

x-(-9x^2-5x+3)=0

We get rid of parentheses

9x^2+5x+x-3=0

We add all the numbers together, and all the variables

9x^2+6x-3=0

a = 9; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·9·(-3)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12}{2*9}=\frac{-18}{18}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12}{2*9}=\frac{6}{18}
=1/3
$