X2*122=(2+x)2

Solution for X2*122=(2+x)2 equation:

X2*122=(2+X)2

We move all terms to the left:

X2*122-((2+X)2)=0

We add all the numbers together, and all the variables

X2*122-((X+2)2)=0

Wy multiply elements

122X^2-((X+2)2)=0


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

(X+2)2

We multiply parentheses

2X+4

Back to the equation:

-(2X+4)


We get rid of parentheses

122X^2-2X-4=0

a = 122; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·122·(-4)
Δ = 1956
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:

$\sqrt{\Delta}=\sqrt{1956}=\sqrt{4*489}=\sqrt{4}*\sqrt{489}=2\sqrt{489}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{489}}{2*122}=\frac{2-2\sqrt{489}}{244}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{489}}{2*122}=\frac{2+2\sqrt{489}}{244}
$