(6x+5)(9x-4)=0

Solution for (6x+5)(9x-4)=0 equation:

(6x+5)(9x-4)=0

We multiply parentheses ..

(+54x^2-24x+45x-20)=0

We get rid of parentheses

54x^2-24x+45x-20=0

We add all the numbers together, and all the variables

54x^2+21x-20=0

a = 54; b = 21; c = -20;
Δ = b2-4ac
Δ = 212-4·54·(-20)
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{-(21)-69}{2*54}=\frac{-90}{108}
=-5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+69}{2*54}=\frac{48}{108}
=4/9
$