(5x-9)(7x+6)=0

Solution for (5x-9)(7x+6)=0 equation:

(5x-9)(7x+6)=0

We multiply parentheses ..

(+35x^2+30x-63x-54)=0

We get rid of parentheses

35x^2+30x-63x-54=0

We add all the numbers together, and all the variables

35x^2-33x-54=0

a = 35; b = -33; c = -54;
Δ = b2-4ac
Δ = -332-4·35·(-54)
Δ = 8649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8649}=93$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-93}{2*35}=\frac{-60}{70}
=-6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+93}{2*35}=\frac{126}{70}
=1+4/5
$