X2+x=51

Solution for X2+x=51 equation:

X2+X=51

We move all terms to the left:

X2+X-(51)=0

We add all the numbers together, and all the variables

X^2+X-51=0

a = 1; b = 1; c = -51;
Δ = b2-4ac
Δ = 12-4·1·(-51)
Δ = 205
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{205}}{2*1}=\frac{-1-\sqrt{205}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{205}}{2*1}=\frac{-1+\sqrt{205}}{2}
$