2=8/7+x^2

Solution for 2=8/7+x^2 equation:

2=8/7+x^2

We move all terms to the left:

2-(8/7+x^2)=0


Domain of the equation: 7+x^2)!=0

We move all terms containing x to the left, all other terms to the right

x^2)!=-7

x!=-7/1

x!=-7

x∈R


We get rid of parentheses

-x^2+2-8/7=0

We multiply all the terms by the denominator


-x^2*7-8+2*7=0

We add all the numbers together, and all the variables

-x^2*7+6=0

Wy multiply elements

-7x^2+6=0

a = -7; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-7)·6
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*-7}=\frac{0-2\sqrt{42}}{-14}
=-\frac{2\sqrt{42}}{-14}
=-\frac{\sqrt{42}}{-7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*-7}=\frac{0+2\sqrt{42}}{-14}
=\frac{2\sqrt{42}}{-14}
=\frac{\sqrt{42}}{-7}
$