(7x+6)(3x+8)=0

Solution for (7x+6)(3x+8)=0 equation:

(7x+6)(3x+8)=0

We multiply parentheses ..

(+21x^2+56x+18x+48)=0

We get rid of parentheses

21x^2+56x+18x+48=0

We add all the numbers together, and all the variables

21x^2+74x+48=0

a = 21; b = 74; c = +48;
Δ = b2-4ac
Δ = 742-4·21·48
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(74)-38}{2*21}=\frac{-112}{42}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(74)+38}{2*21}=\frac{-36}{42}
=-6/7
$