x(4-x)=7x+2

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

x(4-x)=7x+2

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-3x-2=0

a = -1; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·(-1)·(-2)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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