6x^2+19x+90.25=110.25

Solution for 6x^2+19x+90.25=110.25 equation:

Simplifying
6x2 + 19x + 90.25 = 110.25

Reorder the terms:
90.25 + 19x + 6x2 = 110.25

Solving
90.25 + 19x + 6x2 = 110.25

Solving for variable 'x'.

Reorder the terms:
90.25 + -110.25 + 19x + 6x2 = 110.25 + -110.25

Combine like terms: 90.25 + -110.25 = -20
-20 + 19x + 6x2 = 110.25 + -110.25

Combine like terms: 110.25 + -110.25 = 0.00
-20 + 19x + 6x2 = 0.00

Factor a trinomial.
(-4 + -1x)(5 + -6x) = 0.00

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(5 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 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 + -6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x = 0 + -5
-6x = 0 + -5

Combine like terms: 0 + -5 = -5
-6x = -5

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333
Solution
x = {-4, 0.8333333333}