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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

15x^2+28x+12=0

a = 15; b = 28; c = +12;
Δ = b2-4ac
Δ = 282-4·15·12
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-8}{2*15}=\frac{-36}{30}
=-1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+8}{2*15}=\frac{-20}{30}
=-2/3
$