(3m+4)(7m+6)=0

Solution for (3m+4)(7m+6)=0 equation:

(3m+4)(7m+6)=0

We multiply parentheses ..

(+21m^2+18m+28m+24)=0

We get rid of parentheses

21m^2+18m+28m+24=0

We add all the numbers together, and all the variables

21m^2+46m+24=0

a = 21; b = 46; c = +24;
Δ = b2-4ac
Δ = 462-4·21·24
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-10}{2*21}=\frac{-56}{42}
=-1+1/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+10}{2*21}=\frac{-36}{42}
=-6/7
$