542=x2+X

Solution for 542=x2+X equation:

542=x2+x

We move all terms to the left:

542-(x2+x)=0

We add all the numbers together, and all the variables

-(+x^2+x)+542=0

We get rid of parentheses

-x^2-x+542=0

We add all the numbers together, and all the variables

-1x^2-1x+542=0

a = -1; b = -1; c = +542;
Δ = b2-4ac
Δ = -12-4·(-1)·542
Δ = 2169
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:

$\sqrt{\Delta}=\sqrt{2169}=\sqrt{9*241}=\sqrt{9}*\sqrt{241}=3\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{241}}{2*-1}=\frac{1-3\sqrt{241}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{241}}{2*-1}=\frac{1+3\sqrt{241}}{-2}
$