(X+10)(x-4)=(2x+4)

Solution for (X+10)(x-4)=(2x+4) equation:

(X+10)(X-4)=(2X+4)

We move all terms to the left:

(X+10)(X-4)-((2X+4))=0

We multiply parentheses ..

(+X^2-4X+10X-40)-((2X+4))=0


We calculate terms in parentheses: -((2X+4)), so:

(2X+4)

We get rid of parentheses

2X+4

Back to the equation:

-(2X+4)


We get rid of parentheses

X^2-4X+10X-2X-40-4=0

We add all the numbers together, and all the variables

X^2+4X-44=0

a = 1; b = 4; c = -44;
Δ = b2-4ac
Δ = 42-4·1·(-44)
Δ = 192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{3}}{2*1}=\frac{-4-8\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{3}}{2*1}=\frac{-4+8\sqrt{3}}{2}
$