3.25x^2=16

Solution for 3.25x^2=16 equation:

3.25x^2=16

We move all terms to the left:

3.25x^2-(16)=0

a = 3.25; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·3.25·(-16)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{13}}{2*3.25}=\frac{0-4\sqrt{13}}{6.5}
=-\frac{4\sqrt{13}}{6.5}
=-\frac{2\sqrt{13}}{3.25}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{13}}{2*3.25}=\frac{0+4\sqrt{13}}{6.5}
=\frac{4\sqrt{13}}{6.5}
=\frac{2\sqrt{13}}{3.25}
$