3.25x^2=9

Solution for 3.25x^2=9 equation:

3.25x^2=9

We move all terms to the left:

3.25x^2-(9)=0

a = 3.25; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·3.25·(-9)
Δ = 117
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:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{13}}{2*3.25}=\frac{0-3\sqrt{13}}{6.5}
=-\frac{3\sqrt{13}}{6.5}
=-\frac{\sqrt{13}}{2.1666666666667}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{13}}{2*3.25}=\frac{0+3\sqrt{13}}{6.5}
=\frac{3\sqrt{13}}{6.5}
=\frac{\sqrt{13}}{2.1666666666667}
$