7x^2-7=462

Solution for 7x^2-7=462 equation:

7x^2-7=462

We move all terms to the left:

7x^2-7-(462)=0

We add all the numbers together, and all the variables

7x^2-469=0

a = 7; b = 0; c = -469;
Δ = b2-4ac
Δ = 02-4·7·(-469)
Δ = 13132
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:

$\sqrt{\Delta}=\sqrt{13132}=\sqrt{196*67}=\sqrt{196}*\sqrt{67}=14\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{67}}{2*7}=\frac{0-14\sqrt{67}}{14}
=-\frac{14\sqrt{67}}{14}
=-\sqrt{67}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{67}}{2*7}=\frac{0+14\sqrt{67}}{14}
=\frac{14\sqrt{67}}{14}
=\sqrt{67}
$