90+(x+37)(x+67)=180

Solution for 90+(x+37)(x+67)=180 equation:

90+(x+37)(x+67)=180

We move all terms to the left:

90+(x+37)(x+67)-(180)=0

We add all the numbers together, and all the variables

(x+37)(x+67)-90=0

We multiply parentheses ..

(+x^2+67x+37x+2479)-90=0

We get rid of parentheses

x^2+67x+37x+2479-90=0

We add all the numbers together, and all the variables

x^2+104x+2389=0

a = 1; b = 104; c = +2389;
Δ = b2-4ac
Δ = 1042-4·1·2389
Δ = 1260
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:

$\sqrt{\Delta}=\sqrt{1260}=\sqrt{36*35}=\sqrt{36}*\sqrt{35}=6\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(104)-6\sqrt{35}}{2*1}=\frac{-104-6\sqrt{35}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(104)+6\sqrt{35}}{2*1}=\frac{-104+6\sqrt{35}}{2}
$