588=7x+x^2

Solution for 588=7x+x^2 equation:

588=7x+x^2

We move all terms to the left:

588-(7x+x^2)=0

We get rid of parentheses

-x^2-7x+588=0

We add all the numbers together, and all the variables

-1x^2-7x+588=0

a = -1; b = -7; c = +588;
Δ = b2-4ac
Δ = -72-4·(-1)·588
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-49}{2*-1}=\frac{-42}{-2}
=+21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+49}{2*-1}=\frac{56}{-2}
=-28
$