16x2=109

Solution for 16x2=109 equation:

16x^2=109

We move all terms to the left:

16x^2-(109)=0

a = 16; b = 0; c = -109;
Δ = b2-4ac
Δ = 02-4·16·(-109)
Δ = 6976
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:

$\sqrt{\Delta}=\sqrt{6976}=\sqrt{64*109}=\sqrt{64}*\sqrt{109}=8\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{109}}{2*16}=\frac{0-8\sqrt{109}}{32}
=-\frac{8\sqrt{109}}{32}
=-\frac{\sqrt{109}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{109}}{2*16}=\frac{0+8\sqrt{109}}{32}
=\frac{8\sqrt{109}}{32}
=\frac{\sqrt{109}}{4}
$