5x^2-12x+11=x^2+6

Solution for 5x^2-12x+11=x^2+6 equation:

5x^2-12x+11=x^2+6

We move all terms to the left:

5x^2-12x+11-(x^2+6)=0

We get rid of parentheses

5x^2-x^2-12x-6+11=0

We add all the numbers together, and all the variables

4x^2-12x+5=0

a = 4; b = -12; c = +5;
Δ = b2-4ac
Δ = -122-4·4·5
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8}{2*4}=\frac{4}{8}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8}{2*4}=\frac{20}{8}
=2+1/2
$