(6-x)-(x^2-6x+10)=0

Solution for (6-x)-(x^2-6x+10)=0 equation:

(6-x)-(x^2-6x+10)=0

We add all the numbers together, and all the variables

(-1x+6)-(x^2-6x+10)=0

We get rid of parentheses

-x^2-1x+6x+6-10=0

We add all the numbers together, and all the variables

-1x^2+5x-4=0

a = -1; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·(-1)·(-4)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3}{2*-1}=\frac{-2}{-2}
=1
$