180=x+9*x*x-4

Solution for 180=x+9*x*x-4 equation:

180=x+9x*x-4

We move all terms to the left:

180-(x+9x*x-4)=0

We get rid of parentheses

-x-9x*x+4+180=0

We add all the numbers together, and all the variables

-1x-9x*x+184=0

Wy multiply elements

-9x^2-1x+184=0

a = -9; b = -1; c = +184;
Δ = b2-4ac
Δ = -12-4·(-9)·184
Δ = 6625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6625}=\sqrt{25*265}=\sqrt{25}*\sqrt{265}=5\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5\sqrt{265}}{2*-9}=\frac{1-5\sqrt{265}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5\sqrt{265}}{2*-9}=\frac{1+5\sqrt{265}}{-18}
$