8x+38=-3x(-6-4x)

Solution for 8x+38=-3x(-6-4x) equation:

8x+38=-3x(-6-4x)

We move all terms to the left:

8x+38-(-3x(-6-4x))=0

We add all the numbers together, and all the variables

8x-(-3x(-4x-6))+38=0


We calculate terms in parentheses: -(-3x(-4x-6)), so:

-3x(-4x-6)

We multiply parentheses

12x^2+18x

Back to the equation:

-(12x^2+18x)


We get rid of parentheses

-12x^2+8x-18x+38=0

We add all the numbers together, and all the variables

-12x^2-10x+38=0

a = -12; b = -10; c = +38;
Δ = b2-4ac
Δ = -102-4·(-12)·38
Δ = 1924
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:

$\sqrt{\Delta}=\sqrt{1924}=\sqrt{4*481}=\sqrt{4}*\sqrt{481}=2\sqrt{481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{481}}{2*-12}=\frac{10-2\sqrt{481}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{481}}{2*-12}=\frac{10+2\sqrt{481}}{-24}
$