(3x+4)(13x-16)=0

Solution for (3x+4)(13x-16)=0 equation:

(3x+4)(13x-16)=0

We multiply parentheses ..

(+39x^2-48x+52x-64)=0

We get rid of parentheses

39x^2-48x+52x-64=0

We add all the numbers together, and all the variables

39x^2+4x-64=0

a = 39; b = 4; c = -64;
Δ = b2-4ac
Δ = 42-4·39·(-64)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-100}{2*39}=\frac{-104}{78}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+100}{2*39}=\frac{96}{78}
=1+3/13
$