65x^2=9

Solution for 65x^2=9 equation:

65x^2=9

We move all terms to the left:

65x^2-(9)=0

a = 65; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·65·(-9)
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{65}}{2*65}=\frac{0-6\sqrt{65}}{130}
=-\frac{6\sqrt{65}}{130}
=-\frac{3\sqrt{65}}{65}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{65}}{2*65}=\frac{0+6\sqrt{65}}{130}
=\frac{6\sqrt{65}}{130}
=\frac{3\sqrt{65}}{65}
$