X^2+6-11=9x-1

Solution for X^2+6-11=9x-1 equation:

X^2+6-11=9X-1

We move all terms to the left:

X^2+6-11-(9X-1)=0

We add all the numbers together, and all the variables

X^2-(9X-1)-5=0

We get rid of parentheses

X^2-9X+1-5=0

We add all the numbers together, and all the variables

X^2-9X-4=0

a = 1; b = -9; c = -4;
Δ = b2-4ac
Δ = -92-4·1·(-4)
Δ = 97
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{-(-9)-\sqrt{97}}{2*1}=\frac{9-\sqrt{97}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{97}}{2*1}=\frac{9+\sqrt{97}}{2}
$