9-x^2=14-6x

Solution for 9-x^2=14-6x equation:

9-x^2=14-6x

We move all terms to the left:

9-x^2-(14-6x)=0

We add all the numbers together, and all the variables

-x^2-(-6x+14)+9=0

We add all the numbers together, and all the variables

-1x^2-(-6x+14)+9=0

We get rid of parentheses

-1x^2+6x-14+9=0

We add all the numbers together, and all the variables

-1x^2+6x-5=0

a = -1; b = 6; c = -5;
Δ = b2-4ac
Δ = 62-4·(-1)·(-5)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4}{2*-1}=\frac{-10}{-2}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4}{2*-1}=\frac{-2}{-2}
=1
$