(x+1)(4-x)=6x

Solution for (x+1)(4-x)=6x equation:

(x+1)(4-x)=6x

We move all terms to the left:

(x+1)(4-x)-(6x)=0

We add all the numbers together, and all the variables

(x+1)(-1x+4)-6x=0

We add all the numbers together, and all the variables

-6x+(x+1)(-1x+4)=0

We multiply parentheses ..

(-1x^2+4x-1x+4)-6x=0

We get rid of parentheses

-1x^2+4x-1x-6x+4=0

We add all the numbers together, and all the variables

-1x^2-3x+4=0

a = -1; b = -3; c = +4;
Δ = b2-4ac
Δ = -32-4·(-1)·4
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-5}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5}{2*-1}=\frac{8}{-2}
=-4
$