(3x-14)(9x+20)=0

Solution for (3x-14)(9x+20)=0 equation:

(3x-14)(9x+20)=0

We multiply parentheses ..

(+27x^2+60x-126x-280)=0

We get rid of parentheses

27x^2+60x-126x-280=0

We add all the numbers together, and all the variables

27x^2-66x-280=0

a = 27; b = -66; c = -280;
Δ = b2-4ac
Δ = -662-4·27·(-280)
Δ = 34596
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{34596}=186$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-186}{2*27}=\frac{-120}{54}
=-2+2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+186}{2*27}=\frac{252}{54}
=4+2/3
$