X+38=2x(6+x)

Solution for X+38=2x(6+x) equation:

X+38=2X(6+X)

We move all terms to the left:

X+38-(2X(6+X))=0

We add all the numbers together, and all the variables

X-(2X(X+6))+38=0


We calculate terms in parentheses: -(2X(X+6)), so:

2X(X+6)

We multiply parentheses

2X^2+12X

Back to the equation:

-(2X^2+12X)


We get rid of parentheses

-2X^2+X-12X+38=0

We add all the numbers together, and all the variables

-2X^2-11X+38=0

a = -2; b = -11; c = +38;
Δ = b2-4ac
Δ = -112-4·(-2)·38
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-5\sqrt{17}}{2*-2}=\frac{11-5\sqrt{17}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5\sqrt{17}}{2*-2}=\frac{11+5\sqrt{17}}{-4}
$