(x+3)(4-x)=5x

Solution for (x+3)(4-x)=5x equation:

(x+3)(4-x)=5x

We move all terms to the left:

(x+3)(4-x)-(5x)=0

We add all the numbers together, and all the variables

(x+3)(-1x+4)-5x=0

We add all the numbers together, and all the variables

-5x+(x+3)(-1x+4)=0

We multiply parentheses ..

(-1x^2+4x-3x+12)-5x=0

We get rid of parentheses

-1x^2+4x-3x-5x+12=0

We add all the numbers together, and all the variables

-1x^2-4x+12=0

a = -1; b = -4; c = +12;
Δ = b2-4ac
Δ = -42-4·(-1)·12
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*-1}=\frac{-4}{-2}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*-1}=\frac{12}{-2}
=-6
$