30-5x=x^2

Solution for 30-5x=x^2 equation:

30-5x=x^2

We move all terms to the left:

30-5x-(x^2)=0

determiningTheFunctionDomain
-x^2-5x+30=0

We add all the numbers together, and all the variables

-1x^2-5x+30=0

a = -1; b = -5; c = +30;
Δ = b2-4ac
Δ = -52-4·(-1)·30
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{145}}{2*-1}=\frac{5-\sqrt{145}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{145}}{2*-1}=\frac{5+\sqrt{145}}{-2}
$