(x*x)-x=30

Solution for (x*x)-x=30 equation:

(x*x)-x=30

We move all terms to the left:

(x*x)-x-(30)=0

We add all the numbers together, and all the variables

(+x*x)-x-30=0

We add all the numbers together, and all the variables

-1x+(+x*x)-30=0

We get rid of parentheses

-1x+x*x-30=0

Wy multiply elements

x^2-1x-30=0

a = 1; b = -1; c = -30;
Δ = b2-4ac
Δ = -12-4·1·(-30)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*1}=\frac{12}{2}
=6
$