(2x-7)(9x+3)=0

Solution for (2x-7)(9x+3)=0 equation:

(2x-7)(9x+3)=0

We multiply parentheses ..

(+18x^2+6x-63x-21)=0

We get rid of parentheses

18x^2+6x-63x-21=0

We add all the numbers together, and all the variables

18x^2-57x-21=0

a = 18; b = -57; c = -21;
Δ = b2-4ac
Δ = -572-4·18·(-21)
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-69}{2*18}=\frac{-12}{36}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+69}{2*18}=\frac{126}{36}
=3+1/2
$