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

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

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

We multiply parentheses ..

(+15x^2-25x-18x+30)=0

We get rid of parentheses

15x^2-25x-18x+30=0

We add all the numbers together, and all the variables

15x^2-43x+30=0

a = 15; b = -43; c = +30;
Δ = b2-4ac
Δ = -432-4·15·30
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-7}{2*15}=\frac{36}{30}
=1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+7}{2*15}=\frac{50}{30}
=1+2/3
$