(x2)=(103+x)

Solution for (x2)=(103+x) equation:

(x2)=(103+x)

We move all terms to the left:

(x2)-((103+x))=0

We add all the numbers together, and all the variables

x2-((x+103))=0

We add all the numbers together, and all the variables

x^2-((x+103))=0


We calculate terms in parentheses: -((x+103)), so:

(x+103)

We get rid of parentheses

x+103

Back to the equation:

-(x+103)


We get rid of parentheses

x^2-x-103=0

We add all the numbers together, and all the variables

x^2-1x-103=0

a = 1; b = -1; c = -103;
Δ = b2-4ac
Δ = -12-4·1·(-103)
Δ = 413
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{413}}{2*1}=\frac{1-\sqrt{413}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{413}}{2*1}=\frac{1+\sqrt{413}}{2}
$