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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-3(4x+6)-(5x(x+3))=0

We multiply parentheses

-12x-(5x(x+3))-18=0


We calculate terms in parentheses: -(5x(x+3)), so:

5x(x+3)

We multiply parentheses

5x^2+15x

Back to the equation:

-(5x^2+15x)


We get rid of parentheses

-5x^2-12x-15x-18=0

We add all the numbers together, and all the variables

-5x^2-27x-18=0

a = -5; b = -27; c = -18;
Δ = b2-4ac
Δ = -272-4·(-5)·(-18)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{41}}{2*-5}=\frac{27-3\sqrt{41}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{41}}{2*-5}=\frac{27+3\sqrt{41}}{-10}
$