6x^2-17=-12

Solution for 6x^2-17=-12 equation:

6x^2-17=-12

We move all terms to the left:

6x^2-17-(-12)=0

We add all the numbers together, and all the variables

6x^2-5=0

a = 6; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·6·(-5)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*6}=\frac{0-2\sqrt{30}}{12}
=-\frac{2\sqrt{30}}{12}
=-\frac{\sqrt{30}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*6}=\frac{0+2\sqrt{30}}{12}
=\frac{2\sqrt{30}}{12}
=\frac{\sqrt{30}}{6}
$