(3x-5)(4x-6)=0

Solution for (3x-5)(4x-6)=0 equation:

(3x-5)(4x-6)=0

We multiply parentheses ..

(+12x^2-18x-20x+30)=0

We get rid of parentheses

12x^2-18x-20x+30=0

We add all the numbers together, and all the variables

12x^2-38x+30=0

a = 12; b = -38; c = +30;
Δ = b2-4ac
Δ = -382-4·12·30
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2}{2*12}=\frac{36}{24}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2}{2*12}=\frac{40}{24}
=1+2/3
$