2(2x-1)(3x+5)=0

Solution for 2(2x-1)(3x+5)=0 equation:

2(2x-1)(3x+5)=0

We multiply parentheses ..

2(+6x^2+10x-3x-5)=0

We multiply parentheses

12x^2+20x-6x-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{-40}{24}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+26}{2*12}=\frac{12}{24}
=1/2
$