2(x^2-1)=98.x

Solution for 2(x^2-1)=98.x equation:

2(x^2-1)=98.x

We move all terms to the left:

2(x^2-1)-(98.x)=0

We add all the numbers together, and all the variables

2(x^2-1)-(+98.x)=0

We multiply parentheses

2x^2-(+98.x)-2=0

We get rid of parentheses

2x^2-98.x-2=0

We add all the numbers together, and all the variables

2x^2-98x-2=0

a = 2; b = -98; c = -2;
Δ = b2-4ac
Δ = -982-4·2·(-2)
Δ = 9620
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:

$\sqrt{\Delta}=\sqrt{9620}=\sqrt{4*2405}=\sqrt{4}*\sqrt{2405}=2\sqrt{2405}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-2\sqrt{2405}}{2*2}=\frac{98-2\sqrt{2405}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+2\sqrt{2405}}{2*2}=\frac{98+2\sqrt{2405}}{4}
$