20x-70=x^2+30

Solution for 20x-70=x^2+30 equation:

Simplifying
20x + -70 = x2 + 30

Reorder the terms:
-70 + 20x = x2 + 30

Reorder the terms:
-70 + 20x = 30 + x2

Solving
-70 + 20x = 30 + x2

Solving for variable 'x'.

Reorder the terms:
-70 + -30 + 20x + -1x2 = 30 + x2 + -30 + -1x2

Combine like terms: -70 + -30 = -100
-100 + 20x + -1x2 = 30 + x2 + -30 + -1x2

Reorder the terms:
-100 + 20x + -1x2 = 30 + -30 + x2 + -1x2

Combine like terms: 30 + -30 = 0
-100 + 20x + -1x2 = 0 + x2 + -1x2
-100 + 20x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-100 + 20x + -1x2 = 0

Factor a trinomial.
(-10 + x)(10 + -1x) = 0

Subproblem 1
Set the factor '(-10 + x)' equal to zero and attempt to solve:

Simplifying
-10 + x = 0

Solving
-10 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '10' to each side of the equation.
-10 + 10 + x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + x = 0 + 10
x = 0 + 10

Combine like terms: 0 + 10 = 10
x = 10

Simplifying
x = 10
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {10, 10}