2x-5=-x(6+3x)

Solution for 2x-5=-x(6+3x) equation:

2x-5=-x(6+3x)

We move all terms to the left:

2x-5-(-x(6+3x))=0

We add all the numbers together, and all the variables

2x-(-x(3x+6))-5=0


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

-x(3x+6)

We multiply parentheses

-3x^2-6x

Back to the equation:

-(-3x^2-6x)


We get rid of parentheses

3x^2+6x+2x-5=0

We add all the numbers together, and all the variables

3x^2+8x-5=0

a = 3; b = 8; c = -5;
Δ = b2-4ac
Δ = 82-4·3·(-5)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{31}}{2*3}=\frac{-8-2\sqrt{31}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{31}}{2*3}=\frac{-8+2\sqrt{31}}{6}
$