X(4x+9)=180

Solution for X(4x+9)=180 equation:

X(4X+9)=180

We move all terms to the left:

X(4X+9)-(180)=0

We multiply parentheses

4X^2+9X-180=0

a = 4; b = 9; c = -180;
Δ = b2-4ac
Δ = 92-4·4·(-180)
Δ = 2961
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:

$\sqrt{\Delta}=\sqrt{2961}=\sqrt{9*329}=\sqrt{9}*\sqrt{329}=3\sqrt{329}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{329}}{2*4}=\frac{-9-3\sqrt{329}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{329}}{2*4}=\frac{-9+3\sqrt{329}}{8}
$