(6x+2)(4x+3)=0

Solution for (6x+2)(4x+3)=0 equation:

(6x+2)(4x+3)=0

We multiply parentheses ..

(+24x^2+18x+8x+6)=0

We get rid of parentheses

24x^2+18x+8x+6=0

We add all the numbers together, and all the variables

24x^2+26x+6=0

a = 24; b = 26; c = +6;
Δ = b2-4ac
Δ = 262-4·24·6
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-10}{2*24}=\frac{-36}{48}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+10}{2*24}=\frac{-16}{48}
=-1/3
$