(9x-5)(6x+3)=0

Solution for (9x-5)(6x+3)=0 equation:

(9x-5)(6x+3)=0

We multiply parentheses ..

(+54x^2+27x-30x-15)=0

We get rid of parentheses

54x^2+27x-30x-15=0

We add all the numbers together, and all the variables

54x^2-3x-15=0

a = 54; b = -3; c = -15;
Δ = b2-4ac
Δ = -32-4·54·(-15)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-57}{2*54}=\frac{-54}{108}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+57}{2*54}=\frac{60}{108}
=5/9
$