0=-x^2-x+4088

Solution for 0=-x^2-x+4088 equation:

0=-x^2-x+4088

We move all terms to the left:

0-(-x^2-x+4088)=0

We add all the numbers together, and all the variables

-(-x^2-x+4088)=0

We get rid of parentheses

x^2+x-4088=0

a = 1; b = 1; c = -4088;
Δ = b2-4ac
Δ = 12-4·1·(-4088)
Δ = 16353
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:

$\sqrt{\Delta}=\sqrt{16353}=\sqrt{9*1817}=\sqrt{9}*\sqrt{1817}=3\sqrt{1817}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{1817}}{2*1}=\frac{-1-3\sqrt{1817}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{1817}}{2*1}=\frac{-1+3\sqrt{1817}}{2}
$