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

Solution for (3x-2)(5+6x)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+18x^2+15x-12x-10)=0

We get rid of parentheses

18x^2+15x-12x-10=0

We add all the numbers together, and all the variables

18x^2+3x-10=0

a = 18; b = 3; c = -10;
Δ = b2-4ac
Δ = 32-4·18·(-10)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-27}{2*18}=\frac{-30}{36}
=-5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+27}{2*18}=\frac{24}{36}
=2/3
$