(4/a-7)(3a+8)=0

Solution for (4/a-7)(3a+8)=0 equation:

(4/a-7)(3a+8)=0


Domain of the equation: a-7)(3a+8)!=0

a∈R


We multiply parentheses ..

(+12a^2+32a-21a-56)=0

We get rid of parentheses

12a^2+32a-21a-56=0

We add all the numbers together, and all the variables

12a^2+11a-56=0

a = 12; b = 11; c = -56;
Δ = b2-4ac
Δ = 112-4·12·(-56)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-53}{2*12}=\frac{-64}{24}
=-2+2/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+53}{2*12}=\frac{42}{24}
=1+3/4
$