5x-x^2=7x-63

Solution for 5x-x^2=7x-63 equation:

5x-x^2=7x-63

We move all terms to the left:

5x-x^2-(7x-63)=0

We add all the numbers together, and all the variables

-1x^2+5x-(7x-63)=0

We get rid of parentheses

-1x^2+5x-7x+63=0

We add all the numbers together, and all the variables

-1x^2-2x+63=0

a = -1; b = -2; c = +63;
Δ = b2-4ac
Δ = -22-4·(-1)·63
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-16}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+16}{2*-1}=\frac{18}{-2}
=-9
$