X^2-28x+196=6

Solution for X^2-28x+196=6 equation:

X^2-28X+196=6

We move all terms to the left:

X^2-28X+196-(6)=0

We add all the numbers together, and all the variables

X^2-28X+190=0

a = 1; b = -28; c = +190;
Δ = b2-4ac
Δ = -282-4·1·190
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{-(-28)-2\sqrt{6}}{2*1}=\frac{28-2\sqrt{6}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{6}}{2*1}=\frac{28+2\sqrt{6}}{2}
$