(8x-5)(9x-7)=0

Solution for (8x-5)(9x-7)=0 equation:

(8x-5)(9x-7)=0

We multiply parentheses ..

(+72x^2-56x-45x+35)=0

We get rid of parentheses

72x^2-56x-45x+35=0

We add all the numbers together, and all the variables

72x^2-101x+35=0

a = 72; b = -101; c = +35;
Δ = b2-4ac
Δ = -1012-4·72·35
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-101)-11}{2*72}=\frac{90}{144}
=5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-101)+11}{2*72}=\frac{112}{144}
=7/9
$