(x)=x^2+7x+6

Solution for (x)=x^2+7x+6 equation:

(x)=x^2+7x+6

We move all terms to the left:

(x)-(x^2+7x+6)=0

We get rid of parentheses

-x^2+x-7x-6=0

We add all the numbers together, and all the variables

-1x^2-6x-6=0

a = -1; b = -6; c = -6;
Δ = b2-4ac
Δ = -62-4·(-1)·(-6)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{3}}{2*-1}=\frac{6-2\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{3}}{2*-1}=\frac{6+2\sqrt{3}}{-2}
$