(x-4)(7-x)=5-x*2

Solution for (x-4)(7-x)=5-x*2 equation:

(x-4)(7-x)=5-x*2

We move all terms to the left:

(x-4)(7-x)-(5-x*2)=0

We add all the numbers together, and all the variables

(x-4)(-1x+7)-(-x*2+5)=0

We get rid of parentheses

(x-4)(-1x+7)+x*2-5=0

We multiply parentheses ..

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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+13x-33=0

a = -1; b = 13; c = -33;
Δ = b2-4ac
Δ = 132-4·(-1)·(-33)
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{37}}{2*-1}=\frac{-13-\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{37}}{2*-1}=\frac{-13+\sqrt{37}}{-2}
$