2(17x-3)(4x+13)=0

Solution for 2(17x-3)(4x+13)=0 equation:

2(17x-3)(4x+13)=0

We multiply parentheses ..

2(+68x^2+221x-12x-39)=0

We multiply parentheses

136x^2+442x-24x-78=0

We add all the numbers together, and all the variables

136x^2+418x-78=0

a = 136; b = 418; c = -78;
Δ = b2-4ac
Δ = 4182-4·136·(-78)
Δ = 217156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{217156}=466$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(418)-466}{2*136}=\frac{-884}{272}
=-3+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(418)+466}{2*136}=\frac{48}{272}
=3/17
$