7x^2+2=352

Solution for 7x^2+2=352 equation:

7x^2+2=352

We move all terms to the left:

7x^2+2-(352)=0

We add all the numbers together, and all the variables

7x^2-350=0

a = 7; b = 0; c = -350;
Δ = b2-4ac
Δ = 02-4·7·(-350)
Δ = 9800
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:

$\sqrt{\Delta}=\sqrt{9800}=\sqrt{4900*2}=\sqrt{4900}*\sqrt{2}=70\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-70\sqrt{2}}{2*7}=\frac{0-70\sqrt{2}}{14}
=-\frac{70\sqrt{2}}{14}
=-5\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+70\sqrt{2}}{2*7}=\frac{0+70\sqrt{2}}{14}
=\frac{70\sqrt{2}}{14}
=5\sqrt{2}
$