x^2-14x=49=4

Solution for x^2-14x=49=4 equation:

x^2-14x=49=4

We move all terms to the left:

x^2-14x-(49)=0

a = 1; b = -14; c = -49;
Δ = b2-4ac
Δ = -142-4·1·(-49)
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14\sqrt{2}}{2*1}=\frac{14-14\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14\sqrt{2}}{2*1}=\frac{14+14\sqrt{2}}{2}
$