2956=x^2+x

Solution for 2956=x^2+x equation:

2956=x^2+x

We move all terms to the left:

2956-(x^2+x)=0

We get rid of parentheses

-x^2-x+2956=0

We add all the numbers together, and all the variables

-1x^2-1x+2956=0

a = -1; b = -1; c = +2956;
Δ = b2-4ac
Δ = -12-4·(-1)·2956
Δ = 11825
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:

$\sqrt{\Delta}=\sqrt{11825}=\sqrt{25*473}=\sqrt{25}*\sqrt{473}=5\sqrt{473}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5\sqrt{473}}{2*-1}=\frac{1-5\sqrt{473}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5\sqrt{473}}{2*-1}=\frac{1+5\sqrt{473}}{-2}
$