2(5x-7)(3x+1)=0

Solution for 2(5x-7)(3x+1)=0 equation:

2(5x-7)(3x+1)=0

We multiply parentheses ..

2(+15x^2+5x-21x-7)=0

We multiply parentheses

30x^2+10x-42x-14=0

We add all the numbers together, and all the variables

30x^2-32x-14=0

a = 30; b = -32; c = -14;
Δ = b2-4ac
Δ = -322-4·30·(-14)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-52}{2*30}=\frac{-20}{60}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+52}{2*30}=\frac{84}{60}
=1+2/5
$