16z^2+137=196z

Solution for 16z^2+137=196z equation:

16z^2+137=196z

We move all terms to the left:

16z^2+137-(196z)=0

a = 16; b = -196; c = +137;
Δ = b2-4ac
Δ = -1962-4·16·137
Δ = 29648
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{29648}=\sqrt{16*1853}=\sqrt{16}*\sqrt{1853}=4\sqrt{1853}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-196)-4\sqrt{1853}}{2*16}=\frac{196-4\sqrt{1853}}{32}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-196)+4\sqrt{1853}}{2*16}=\frac{196+4\sqrt{1853}}{32}
$