5x^2-2=34

Solution for 5x^2-2=34 equation:

5x^2-2=34

We move all terms to the left:

5x^2-2-(34)=0

We add all the numbers together, and all the variables

5x^2-36=0

a = 5; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·5·(-36)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*5}=\frac{0-12\sqrt{5}}{10}
=-\frac{12\sqrt{5}}{10}
=-\frac{6\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*5}=\frac{0+12\sqrt{5}}{10}
=\frac{12\sqrt{5}}{10}
=\frac{6\sqrt{5}}{5}
$