83-12x^2=0

Solution for 83-12x^2=0 equation:

83-12x^2=0

a = -12; b = 0; c = +83;
Δ = b2-4ac
Δ = 02-4·(-12)·83
Δ = 3984
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:

$\sqrt{\Delta}=\sqrt{3984}=\sqrt{16*249}=\sqrt{16}*\sqrt{249}=4\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{249}}{2*-12}=\frac{0-4\sqrt{249}}{-24}
=-\frac{4\sqrt{249}}{-24}
=-\frac{\sqrt{249}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{249}}{2*-12}=\frac{0+4\sqrt{249}}{-24}
=\frac{4\sqrt{249}}{-24}
=\frac{\sqrt{249}}{-6}
$