10x^2=49x+5

Solution for 10x^2=49x+5 equation:

Simplifying
10x2 = 49x + 5

Reorder the terms:
10x2 = 5 + 49x

Solving
10x2 = 5 + 49x

Solving for variable 'x'.

Reorder the terms:
-5 + -49x + 10x2 = 5 + 49x + -5 + -49x

Reorder the terms:
-5 + -49x + 10x2 = 5 + -5 + 49x + -49x

Combine like terms: 5 + -5 = 0
-5 + -49x + 10x2 = 0 + 49x + -49x
-5 + -49x + 10x2 = 49x + -49x

Combine like terms: 49x + -49x = 0
-5 + -49x + 10x2 = 0

Factor a trinomial.
(-1 + -10x)(5 + -1x) = 0

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

Simplifying
-1 + -10x = 0

Solving
-1 + -10x = 0

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

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

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

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

Divide each side by '-10'.
x = -0.1

Simplifying
x = -0.1
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-0.1, 5}