(13x+8)(5x-2)=0

Solution for (13x+8)(5x-2)=0 equation:

(13x+8)(5x-2)=0

We multiply parentheses ..

(+65x^2-26x+40x-16)=0

We get rid of parentheses

65x^2-26x+40x-16=0

We add all the numbers together, and all the variables

65x^2+14x-16=0

a = 65; b = 14; c = -16;
Δ = b2-4ac
Δ = 142-4·65·(-16)
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-66}{2*65}=\frac{-80}{130}
=-8/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+66}{2*65}=\frac{52}{130}
=2/5
$