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

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

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

We move all terms to the left:

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

We multiply parentheses

6x^2+15x-(2(2x+6))=0


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

2(2x+6)

We multiply parentheses

4x+12

Back to the equation:

-(4x+12)


We get rid of parentheses

6x^2+15x-4x-12=0

We add all the numbers together, and all the variables

6x^2+11x-12=0

a = 6; b = 11; c = -12;
Δ = b2-4ac
Δ = 112-4·6·(-12)
Δ = 409
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{-(11)-\sqrt{409}}{2*6}=\frac{-11-\sqrt{409}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{409}}{2*6}=\frac{-11+\sqrt{409}}{12}
$