(3x-2)(5x-7)=0

Solution for (3x-2)(5x-7)=0 equation:

(3x-2)(5x-7)=0

We multiply parentheses ..

(+15x^2-21x-10x+14)=0

We get rid of parentheses

15x^2-21x-10x+14=0

We add all the numbers together, and all the variables

15x^2-31x+14=0

a = 15; b = -31; c = +14;
Δ = b2-4ac
Δ = -312-4·15·14
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{-(-31)-11}{2*15}=\frac{20}{30}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+11}{2*15}=\frac{42}{30}
=1+2/5
$