3x(x+1)=2x(x-5)-6

Solution for 3x(x+1)=2x(x-5)-6 equation:

3x(x+1)=2x(x-5)-6

We move all terms to the left:

3x(x+1)-(2x(x-5)-6)=0

We multiply parentheses

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


We calculate terms in parentheses: -(2x(x-5)-6), so:

2x(x-5)-6

We multiply parentheses

2x^2-10x-6

Back to the equation:

-(2x^2-10x-6)


We get rid of parentheses

3x^2-2x^2+3x+10x+6=0

We add all the numbers together, and all the variables

x^2+13x+6=0

a = 1; b = 13; c = +6;
Δ = b2-4ac
Δ = 132-4·1·6
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{145}}{2*1}=\frac{-13-\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{145}}{2*1}=\frac{-13+\sqrt{145}}{2}
$