(6x-7)(3x-5)=0

Solution for (6x-7)(3x-5)=0 equation:

(6x-7)(3x-5)=0

We multiply parentheses ..

(+18x^2-30x-21x+35)=0

We get rid of parentheses

18x^2-30x-21x+35=0

We add all the numbers together, and all the variables

18x^2-51x+35=0

a = 18; b = -51; c = +35;
Δ = b2-4ac
Δ = -512-4·18·35
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-9}{2*18}=\frac{42}{36}
=1+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+9}{2*18}=\frac{60}{36}
=1+2/3
$