(2x-7)(6x-5)=0

Solution for (2x-7)(6x-5)=0 equation:

(2x-7)(6x-5)=0

We multiply parentheses ..

(+12x^2-10x-42x+35)=0

We get rid of parentheses

12x^2-10x-42x+35=0

We add all the numbers together, and all the variables

12x^2-52x+35=0

a = 12; b = -52; c = +35;
Δ = b2-4ac
Δ = -522-4·12·35
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-32}{2*12}=\frac{20}{24}
=5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+32}{2*12}=\frac{84}{24}
=3+1/2
$