x^2+28x+196=7

Solution for x^2+28x+196=7 equation:

x^2+28x+196=7

We move all terms to the left:

x^2+28x+196-(7)=0

We add all the numbers together, and all the variables

x^2+28x+189=0

a = 1; b = 28; c = +189;
Δ = b2-4ac
Δ = 282-4·1·189
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{7}}{2*1}=\frac{-28-2\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{7}}{2*1}=\frac{-28+2\sqrt{7}}{2}
$