x2+3=x+21

Solution for x2+3=x+21 equation:

x2+3=x+21

We move all terms to the left:

x2+3-(x+21)=0

We add all the numbers together, and all the variables

x^2-(x+21)+3=0

We get rid of parentheses

x^2-x-21+3=0

We add all the numbers together, and all the variables

x^2-1x-18=0

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