x^2-16x=34

Solution for x^2-16x=34 equation:

x^2-16x=34

We move all terms to the left:

x^2-16x-(34)=0

a = 1; b = -16; c = -34;
Δ = b2-4ac
Δ = -162-4·1·(-34)
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{-(-16)-14\sqrt{2}}{2*1}=\frac{16-14\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+14\sqrt{2}}{2*1}=\frac{16+14\sqrt{2}}{2}
$