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

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

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

We multiply parentheses ..

(+4a^2-32a+3a-24)=0

We get rid of parentheses

4a^2-32a+3a-24=0

We add all the numbers together, and all the variables

4a^2-29a-24=0

a = 4; b = -29; c = -24;
Δ = b2-4ac
Δ = -292-4·4·(-24)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-35}{2*4}=\frac{-6}{8}
=-3/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+35}{2*4}=\frac{64}{8}
=8
$