5x^2-6x-11=x^2-9x

Solution for 5x^2-6x-11=x^2-9x equation:

5x^2-6x-11=x^2-9x

We move all terms to the left:

5x^2-6x-11-(x^2-9x)=0

We get rid of parentheses

5x^2-x^2-6x+9x-11=0

We add all the numbers together, and all the variables

4x^2+3x-11=0

a = 4; b = 3; c = -11;
Δ = b2-4ac
Δ = 32-4·4·(-11)
Δ = 185
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{-(3)-\sqrt{185}}{2*4}=\frac{-3-\sqrt{185}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{185}}{2*4}=\frac{-3+\sqrt{185}}{8}
$