-6x(x+3)=3(x-15)

Solution for -6x(x+3)=3(x-15) equation:

-6x(x+3)=3(x-15)

We move all terms to the left:

-6x(x+3)-(3(x-15))=0

We multiply parentheses

-6x^2-18x-(3(x-15))=0


We calculate terms in parentheses: -(3(x-15)), so:

3(x-15)

We multiply parentheses

3x-45

Back to the equation:

-(3x-45)


We get rid of parentheses

-6x^2-18x-3x+45=0

We add all the numbers together, and all the variables

-6x^2-21x+45=0

a = -6; b = -21; c = +45;
Δ = b2-4ac
Δ = -212-4·(-6)·45
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-39}{2*-6}=\frac{-18}{-12}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+39}{2*-6}=\frac{60}{-12}
=-5
$