10x^2-x=x^2+2

Solution for 10x^2-x=x^2+2 equation:

10x^2-x=x^2+2

We move all terms to the left:

10x^2-x-(x^2+2)=0

We add all the numbers together, and all the variables

10x^2-1x-(x^2+2)=0

We get rid of parentheses

10x^2-x^2-1x-2=0

We add all the numbers together, and all the variables

9x^2-1x-2=0

a = 9; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·9·(-2)
Δ = 73
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{73}}{2*9}=\frac{1-\sqrt{73}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{73}}{2*9}=\frac{1+\sqrt{73}}{18}
$