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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+5x^2+10x+4x+8)), so:

(+5x^2+10x+4x+8)

We get rid of parentheses

5x^2+10x+4x+8

We add all the numbers together, and all the variables

5x^2+14x+8

Back to the equation:

-(5x^2+14x+8)


We get rid of parentheses

-5x^2-14x-8+180=0

We add all the numbers together, and all the variables

-5x^2-14x+172=0

a = -5; b = -14; c = +172;
Δ = b2-4ac
Δ = -142-4·(-5)·172
Δ = 3636
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:

$\sqrt{\Delta}=\sqrt{3636}=\sqrt{36*101}=\sqrt{36}*\sqrt{101}=6\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{101}}{2*-5}=\frac{14-6\sqrt{101}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{101}}{2*-5}=\frac{14+6\sqrt{101}}{-10}
$