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

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

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

We multiply parentheses ..

(+18x^2+14x-27x-21)=0

We get rid of parentheses

18x^2+14x-27x-21=0

We add all the numbers together, and all the variables

18x^2-13x-21=0

a = 18; b = -13; c = -21;
Δ = b2-4ac
Δ = -132-4·18·(-21)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-41}{2*18}=\frac{-28}{36}
=-7/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+41}{2*18}=\frac{54}{36}
=1+1/2
$