9x^2-4=85

Solution for 9x^2-4=85 equation:

9x^2-4=85

We move all terms to the left:

9x^2-4-(85)=0

We add all the numbers together, and all the variables

9x^2-89=0

a = 9; b = 0; c = -89;
Δ = b2-4ac
Δ = 02-4·9·(-89)
Δ = 3204
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:

$\sqrt{\Delta}=\sqrt{3204}=\sqrt{36*89}=\sqrt{36}*\sqrt{89}=6\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{89}}{2*9}=\frac{0-6\sqrt{89}}{18}
=-\frac{6\sqrt{89}}{18}
=-\frac{\sqrt{89}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{89}}{2*9}=\frac{0+6\sqrt{89}}{18}
=\frac{6\sqrt{89}}{18}
=\frac{\sqrt{89}}{3}
$