X2+x=4030

Solution for X2+x=4030 equation:

X2+X=4030

We move all terms to the left:

X2+X-(4030)=0

We add all the numbers together, and all the variables

X^2+X-4030=0

a = 1; b = 1; c = -4030;
Δ = b2-4ac
Δ = 12-4·1·(-4030)
Δ = 16121
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:

$\sqrt{\Delta}=\sqrt{16121}=\sqrt{49*329}=\sqrt{49}*\sqrt{329}=7\sqrt{329}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7\sqrt{329}}{2*1}=\frac{-1-7\sqrt{329}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7\sqrt{329}}{2*1}=\frac{-1+7\sqrt{329}}{2}
$