What's a solution with a variable that has no solution

i think you meant to say "whats an equation with a variable that has no solution". if so, then this would be considered a contradiction.

consider the following example

x+3 = x+5

if we subtract x from both sides, they will cancel out and go away

x+3-x = x+5-x

x-x+3 = x-x+5

0x+3 = 0x+5

0+3 = 0+5

3 = 5 this is where the contradiction happens

the last equation above is false regardless of what x value you pick; therefore, there are no solutions to the example equation.

54, jfvhgnjhvnjhcbnncjigjm

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0