4=x^2+6*x+7

Solution for 4=x^2+6*x+7 equation:

4=x^2+6x+7

We move all terms to the left:

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

We get rid of parentheses

-x^2-6x-7+4=0

We add all the numbers together, and all the variables

-1x^2-6x-3=0

a = -1; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·(-1)·(-3)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{6}}{2*-1}=\frac{6-2\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{6}}{2*-1}=\frac{6+2\sqrt{6}}{-2}
$