x2+x=74

Solution for x2+x=74 equation:

x2+x=74

We move all terms to the left:

x2+x-(74)=0

We add all the numbers together, and all the variables

x^2+x-74=0

a = 1; b = 1; c = -74;
Δ = b2-4ac
Δ = 12-4·1·(-74)
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{33}}{2*1}=\frac{-1-3\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{33}}{2*1}=\frac{-1+3\sqrt{33}}{2}
$