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

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

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

We move all terms to the left:

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

We multiply parentheses

-3x^2-15x-(2(x+5))=0


We calculate terms in parentheses: -(2(x+5)), so:

2(x+5)

We multiply parentheses

2x+10

Back to the equation:

-(2x+10)


We get rid of parentheses

-3x^2-15x-2x-10=0

We add all the numbers together, and all the variables

-3x^2-17x-10=0

a = -3; b = -17; c = -10;
Δ = b2-4ac
Δ = -172-4·(-3)·(-10)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-13}{2*-3}=\frac{4}{-6}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+13}{2*-3}=\frac{30}{-6}
=-5
$