(3x+8)(2x+3)=0

Solution for (3x+8)(2x+3)=0 equation:

(3x+8)(2x+3)=0

We multiply parentheses ..

(+6x^2+9x+16x+24)=0

We get rid of parentheses

6x^2+9x+16x+24=0

We add all the numbers together, and all the variables

6x^2+25x+24=0

a = 6; b = 25; c = +24;
Δ = b2-4ac
Δ = 252-4·6·24
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-7}{2*6}=\frac{-32}{12}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+7}{2*6}=\frac{-18}{12}
=-1+1/2
$