9x^2-3=111

Solution for 9x^2-3=111 equation:

9x^2-3=111

We move all terms to the left:

9x^2-3-(111)=0

We add all the numbers together, and all the variables

9x^2-114=0

a = 9; b = 0; c = -114;
Δ = b2-4ac
Δ = 02-4·9·(-114)
Δ = 4104
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:

$\sqrt{\Delta}=\sqrt{4104}=\sqrt{36*114}=\sqrt{36}*\sqrt{114}=6\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{114}}{2*9}=\frac{0-6\sqrt{114}}{18}
=-\frac{6\sqrt{114}}{18}
=-\frac{\sqrt{114}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{114}}{2*9}=\frac{0+6\sqrt{114}}{18}
=\frac{6\sqrt{114}}{18}
=\frac{\sqrt{114}}{3}
$