(6x-5)(5x-12)=0

Solution for (6x-5)(5x-12)=0 equation:

(6x-5)(5x-12)=0

We multiply parentheses ..

(+30x^2-72x-25x+60)=0

We get rid of parentheses

30x^2-72x-25x+60=0

We add all the numbers together, and all the variables

30x^2-97x+60=0

a = 30; b = -97; c = +60;
Δ = b2-4ac
Δ = -972-4·30·60
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-97)-47}{2*30}=\frac{50}{60}
=5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-97)+47}{2*30}=\frac{144}{60}
=2+2/5
$