(4x+5)(x+2)=180

Solution for (4x+5)(x+2)=180 equation:

(4x+5)(x+2)=180

We move all terms to the left:

(4x+5)(x+2)-(180)=0

We multiply parentheses ..

(+4x^2+8x+5x+10)-180=0

We get rid of parentheses

4x^2+8x+5x+10-180=0

We add all the numbers together, and all the variables

4x^2+13x-170=0

a = 4; b = 13; c = -170;
Δ = b2-4ac
Δ = 132-4·4·(-170)
Δ = 2889
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:

$\sqrt{\Delta}=\sqrt{2889}=\sqrt{9*321}=\sqrt{9}*\sqrt{321}=3\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-3\sqrt{321}}{2*4}=\frac{-13-3\sqrt{321}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+3\sqrt{321}}{2*4}=\frac{-13+3\sqrt{321}}{8}
$