3a^2+7=259

Solution for 3a^2+7=259 equation:

3a^2+7=259

We move all terms to the left:

3a^2+7-(259)=0

We add all the numbers together, and all the variables

3a^2-252=0

a = 3; b = 0; c = -252;
Δ = b2-4ac
Δ = 02-4·3·(-252)
Δ = 3024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3024}=\sqrt{144*21}=\sqrt{144}*\sqrt{21}=12\sqrt{21}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{21}}{2*3}=\frac{0-12\sqrt{21}}{6}
=-\frac{12\sqrt{21}}{6}
=-2\sqrt{21}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{21}}{2*3}=\frac{0+12\sqrt{21}}{6}
=\frac{12\sqrt{21}}{6}
=2\sqrt{21}
$