(4x+1)(x+9)=180

Solution for (4x+1)(x+9)=180 equation:

(4x+1)(x+9)=180

We move all terms to the left:

(4x+1)(x+9)-(180)=0

We multiply parentheses ..

(+4x^2+36x+x+9)-180=0

We get rid of parentheses

4x^2+36x+x+9-180=0

We add all the numbers together, and all the variables

4x^2+37x-171=0

a = 4; b = 37; c = -171;
Δ = b2-4ac
Δ = 372-4·4·(-171)
Δ = 4105
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{-(37)-\sqrt{4105}}{2*4}=\frac{-37-\sqrt{4105}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{4105}}{2*4}=\frac{-37+\sqrt{4105}}{8}
$