X^2+c=103

Solution for X^2+c=103 equation:

X^2+X=103

We move all terms to the left:

X^2+X-(103)=0

a = 1; b = 1; c = -103;
Δ = b2-4ac
Δ = 12-4·1·(-103)
Δ = 413
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{413}}{2*1}=\frac{-1-\sqrt{413}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{413}}{2*1}=\frac{-1+\sqrt{413}}{2}
$