(x+37)(x+67)=x

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

(x+37)(x+67)=x

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1x+(x+37)(x+67)=0

We multiply parentheses ..

(+x^2+67x+37x+2479)-1x=0

We get rid of parentheses

x^2+67x+37x-1x+2479=0

We add all the numbers together, and all the variables

x^2+103x+2479=0

a = 1; b = 103; c = +2479;
Δ = b2-4ac
Δ = 1032-4·1·2479
Δ = 693
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:

$\sqrt{\Delta}=\sqrt{693}=\sqrt{9*77}=\sqrt{9}*\sqrt{77}=3\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(103)-3\sqrt{77}}{2*1}=\frac{-103-3\sqrt{77}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(103)+3\sqrt{77}}{2*1}=\frac{-103+3\sqrt{77}}{2}
$