7x2+2=343

Solution for 7x2+2=343 equation:

7x^2+2=343

We move all terms to the left:

7x^2+2-(343)=0

We add all the numbers together, and all the variables

7x^2-341=0

a = 7; b = 0; c = -341;
Δ = b2-4ac
Δ = 02-4·7·(-341)
Δ = 9548
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:

$\sqrt{\Delta}=\sqrt{9548}=\sqrt{4*2387}=\sqrt{4}*\sqrt{2387}=2\sqrt{2387}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2387}}{2*7}=\frac{0-2\sqrt{2387}}{14}
=-\frac{2\sqrt{2387}}{14}
=-\frac{\sqrt{2387}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2387}}{2*7}=\frac{0+2\sqrt{2387}}{14}
=\frac{2\sqrt{2387}}{14}
=\frac{\sqrt{2387}}{7}
$