(x+42)=(x2+1)

Solution for (x+42)=(x2+1) equation:

(x+42)=(x2+1)

We move all terms to the left:

(x+42)-((x2+1))=0

We add all the numbers together, and all the variables

-((+x^2+1))+(x+42)=0

We get rid of parentheses

-((+x^2+1))+x+42=0


We calculate terms in parentheses: -((+x^2+1)), so:

(+x^2+1)

We get rid of parentheses

x^2+1

Back to the equation:

-(x^2+1)


We add all the numbers together, and all the variables

x-(x^2+1)+42=0

We get rid of parentheses

-x^2+x-1+42=0

We add all the numbers together, and all the variables

-1x^2+x+41=0

a = -1; b = 1; c = +41;
Δ = b2-4ac
Δ = 12-4·(-1)·41
Δ = 165
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{165}}{2*-1}=\frac{-1-\sqrt{165}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{165}}{2*-1}=\frac{-1+\sqrt{165}}{-2}
$