x^2-2x+6=9x-4

Solution for x^2-2x+6=9x-4 equation:

x^2-2x+6=9x-4

We move all terms to the left:

x^2-2x+6-(9x-4)=0

We get rid of parentheses

x^2-2x-9x+4+6=0

We add all the numbers together, and all the variables

x^2-11x+10=0

a = 1; b = -11; c = +10;
Δ = b2-4ac
Δ = -112-4·1·10
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-9}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+9}{2*1}=\frac{20}{2}
=10
$