(3x-14)(5x+17)=0

Solution for (3x-14)(5x+17)=0 equation:

(3x-14)(5x+17)=0

We multiply parentheses ..

(+15x^2+51x-70x-238)=0

We get rid of parentheses

15x^2+51x-70x-238=0

We add all the numbers together, and all the variables

15x^2-19x-238=0

a = 15; b = -19; c = -238;
Δ = b2-4ac
Δ = -192-4·15·(-238)
Δ = 14641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14641}=121$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-121}{2*15}=\frac{-102}{30}
=-3+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+121}{2*15}=\frac{140}{30}
=4+2/3
$