x+121=2(x^2+2)

Solution for x+121=2(x^2+2) equation:

x+121=2(x^2+2)

We move all terms to the left:

x+121-(2(x^2+2))=0


We calculate terms in parentheses: -(2(x^2+2)), so:

2(x^2+2)

We multiply parentheses

2x^2+4

Back to the equation:

-(2x^2+4)


We get rid of parentheses

-2x^2+x-4+121=0

We add all the numbers together, and all the variables

-2x^2+x+117=0

a = -2; b = 1; c = +117;
Δ = b2-4ac
Δ = 12-4·(-2)·117
Δ = 937
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{937}}{2*-2}=\frac{-1-\sqrt{937}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{937}}{2*-2}=\frac{-1+\sqrt{937}}{-4}
$