x^2+x=1478

Solution for x^2+x=1478 equation:

x^2+x=1478

We move all terms to the left:

x^2+x-(1478)=0

a = 1; b = 1; c = -1478;
Δ = b2-4ac
Δ = 12-4·1·(-1478)
Δ = 5913
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:

$\sqrt{\Delta}=\sqrt{5913}=\sqrt{81*73}=\sqrt{81}*\sqrt{73}=9\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-9\sqrt{73}}{2*1}=\frac{-1-9\sqrt{73}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+9\sqrt{73}}{2*1}=\frac{-1+9\sqrt{73}}{2}
$