4-7x=x^2

Solution for 4-7x=x^2 equation:

4-7x=x^2

We move all terms to the left:

4-7x-(x^2)=0

determiningTheFunctionDomain
-x^2-7x+4=0

We add all the numbers together, and all the variables

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

a = -1; b = -7; c = +4;
Δ = b2-4ac
Δ = -72-4·(-1)·4
Δ = 65
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{-(-7)-\sqrt{65}}{2*-1}=\frac{7-\sqrt{65}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{65}}{2*-1}=\frac{7+\sqrt{65}}{-2}
$