(5x-17)(7x+20)=0

Solution for (5x-17)(7x+20)=0 equation:

(5x-17)(7x+20)=0

We multiply parentheses ..

(+35x^2+100x-119x-340)=0

We get rid of parentheses

35x^2+100x-119x-340=0

We add all the numbers together, and all the variables

35x^2-19x-340=0

a = 35; b = -19; c = -340;
Δ = b2-4ac
Δ = -192-4·35·(-340)
Δ = 47961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{47961}=219$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-219}{2*35}=\frac{-200}{70}
=-2+6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+219}{2*35}=\frac{238}{70}
=3+2/5
$