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

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

X(X-4)=2(X+7)

We move all terms to the left:

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

We multiply parentheses

X^2-4X-(2(X+7))=0


We calculate terms in parentheses: -(2(X+7)), so:

2(X+7)

We multiply parentheses

2X+14

Back to the equation:

-(2X+14)


We get rid of parentheses

X^2-4X-2X-14=0

We add all the numbers together, and all the variables

X^2-6X-14=0

a = 1; b = -6; c = -14;
Δ = b2-4ac
Δ = -62-4·1·(-14)
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{23}}{2*1}=\frac{6-2\sqrt{23}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{23}}{2*1}=\frac{6+2\sqrt{23}}{2}
$