(X-4)(7-x)=5-x

Solution for (X-4)(7-x)=5-x equation:

(X-4)(7-X)=5-X

We move all terms to the left:

(X-4)(7-X)-(5-X)=0

We add all the numbers together, and all the variables

(X-4)(-1X+7)-(-1X+5)=0

We get rid of parentheses

(X-4)(-1X+7)+1X-5=0

We multiply parentheses ..

(-1X^2+7X+4X-28)+1X-5=0

We add all the numbers together, and all the variables

(-1X^2+7X+4X-28)+X-5=0

We get rid of parentheses

-1X^2+7X+4X+X-28-5=0

We add all the numbers together, and all the variables

-1X^2+12X-33=0

a = -1; b = 12; c = -33;
Δ = b2-4ac
Δ = 122-4·(-1)·(-33)
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{3}}{2*-1}=\frac{-12-2\sqrt{3}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{3}}{2*-1}=\frac{-12+2\sqrt{3}}{-2}
$