(3x-16)(2x+59)=0

Solution for (3x-16)(2x+59)=0 equation:

(3x-16)(2x+59)=0

We multiply parentheses ..

(+6x^2+177x-32x-944)=0

We get rid of parentheses

6x^2+177x-32x-944=0

We add all the numbers together, and all the variables

6x^2+145x-944=0

a = 6; b = 145; c = -944;
Δ = b2-4ac
Δ = 1452-4·6·(-944)
Δ = 43681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{43681}=209$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(145)-209}{2*6}=\frac{-354}{12}
=-29+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(145)+209}{2*6}=\frac{64}{12}
=5+1/3
$