7x^2+2=100

Solution for 7x^2+2=100 equation:

7x^2+2=100

We move all terms to the left:

7x^2+2-(100)=0

We add all the numbers together, and all the variables

7x^2-98=0

a = 7; b = 0; c = -98;
Δ = b2-4ac
Δ = 02-4·7·(-98)
Δ = 2744
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:

$\sqrt{\Delta}=\sqrt{2744}=\sqrt{196*14}=\sqrt{196}*\sqrt{14}=14\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{14}}{2*7}=\frac{0-14\sqrt{14}}{14}
=-\frac{14\sqrt{14}}{14}
=-\sqrt{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{14}}{2*7}=\frac{0+14\sqrt{14}}{14}
=\frac{14\sqrt{14}}{14}
=\sqrt{14}
$