(3a+8)(2a+7)=0

Solution for (3a+8)(2a+7)=0 equation:

(3a+8)(2a+7)=0

We multiply parentheses ..

(+6a^2+21a+16a+56)=0

We get rid of parentheses

6a^2+21a+16a+56=0

We add all the numbers together, and all the variables

6a^2+37a+56=0

a = 6; b = 37; c = +56;
Δ = b2-4ac
Δ = 372-4·6·56
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-5}{2*6}=\frac{-42}{12}
=-3+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+5}{2*6}=\frac{-32}{12}
=-2+2/3
$