(9x-6)(7x+3)=0

Solution for (9x-6)(7x+3)=0 equation:

(9x-6)(7x+3)=0

We multiply parentheses ..

(+63x^2+27x-42x-18)=0

We get rid of parentheses

63x^2+27x-42x-18=0

We add all the numbers together, and all the variables

63x^2-15x-18=0

a = 63; b = -15; c = -18;
Δ = b2-4ac
Δ = -152-4·63·(-18)
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{-(-15)-69}{2*63}=\frac{-54}{126}
=-3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+69}{2*63}=\frac{84}{126}
=2/3
$