(x2+1)2+6=5(x2+1)

Solution for (x2+1)2+6=5(x2+1) equation:

(x2+1)2+6=5(x2+1)

We move all terms to the left:

(x2+1)2+6-(5(x2+1))=0

We add all the numbers together, and all the variables

(+x^2+1)2-(5(+x^2+1))+6=0

We multiply parentheses

2x^2-(5(+x^2+1))+2+6=0


We calculate terms in parentheses: -(5(+x^2+1)), so:

5(+x^2+1)

We multiply parentheses

5x^2+5

Back to the equation:

-(5x^2+5)


We add all the numbers together, and all the variables

2x^2-(5x^2+5)+8=0

We get rid of parentheses

2x^2-5x^2-5+8=0

We add all the numbers together, and all the variables

-3x^2+3=0

a = -3; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-3)·3
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*-3}=\frac{-6}{-6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*-3}=\frac{6}{-6}
=-1
$