30-x=x2+5

Solution for 30-x=x2+5 equation:

30-x=x2+5

We move all terms to the left:

30-x-(x2+5)=0

We add all the numbers together, and all the variables

-(+x^2+5)-x+30=0

We add all the numbers together, and all the variables

-(+x^2+5)-1x+30=0

We get rid of parentheses

-x^2-1x-5+30=0

We add all the numbers together, and all the variables

-1x^2-1x+25=0

a = -1; b = -1; c = +25;
Δ = b2-4ac
Δ = -12-4·(-1)·25
Δ = 101
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{101}}{2*-1}=\frac{1-\sqrt{101}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{101}}{2*-1}=\frac{1+\sqrt{101}}{-2}
$