(3x-5)(4x+2)=0

Solution for (3x-5)(4x+2)=0 equation:

(3x-5)(4x+2)=0

We multiply parentheses ..

(+12x^2+6x-20x-10)=0

We get rid of parentheses

12x^2+6x-20x-10=0

We add all the numbers together, and all the variables

12x^2-14x-10=0

a = 12; b = -14; c = -10;
Δ = b2-4ac
Δ = -142-4·12·(-10)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-26}{2*12}=\frac{-12}{24}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+26}{2*12}=\frac{40}{24}
=1+2/3
$