6x^2-5=289

Solution for 6x^2-5=289 equation:

6x^2-5=289

We move all terms to the left:

6x^2-5-(289)=0

We add all the numbers together, and all the variables

6x^2-294=0

a = 6; b = 0; c = -294;
Δ = b2-4ac
Δ = 02-4·6·(-294)
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-84}{2*6}=\frac{-84}{12}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+84}{2*6}=\frac{84}{12}
=7
$