(3x+5)(8x+4)=0

Solution for (3x+5)(8x+4)=0 equation:

(3x+5)(8x+4)=0

We multiply parentheses ..

(+24x^2+12x+40x+20)=0

We get rid of parentheses

24x^2+12x+40x+20=0

We add all the numbers together, and all the variables

24x^2+52x+20=0

a = 24; b = 52; c = +20;
Δ = b2-4ac
Δ = 522-4·24·20
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-28}{2*24}=\frac{-80}{48}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+28}{2*24}=\frac{-24}{48}
=-1/2
$