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

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

(X+3)(X-4)=4-X

We move all terms to the left:

(X+3)(X-4)-(4-X)=0

We add all the numbers together, and all the variables

(X+3)(X-4)-(-1X+4)=0

We get rid of parentheses

(X+3)(X-4)+1X-4=0

We multiply parentheses ..

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

We add all the numbers together, and all the variables

(+X^2-4X+3X-12)+X-4=0

We get rid of parentheses

X^2-4X+3X+X-12-4=0

We add all the numbers together, and all the variables

X^2-16=0

a = 1; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·1·(-16)
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{-(0)-8}{2*1}=\frac{-8}{2}
=-4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*1}=\frac{8}{2}
=4
$