(2a-1)(4a+3)=0

Solution for (2a-1)(4a+3)=0 equation:

(2a-1)(4a+3)=0

We multiply parentheses ..

(+8a^2+6a-4a-3)=0

We get rid of parentheses

8a^2+6a-4a-3=0

We add all the numbers together, and all the variables

8a^2+2a-3=0

a = 8; b = 2; c = -3;
Δ = b2-4ac
Δ = 22-4·8·(-3)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*8}=\frac{-12}{16}
=-3/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*8}=\frac{8}{16}
=1/2
$