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

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

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

We multiply parentheses ..

(+12x^2+14x-42x-49)=0

We get rid of parentheses

12x^2+14x-42x-49=0

We add all the numbers together, and all the variables

12x^2-28x-49=0

a = 12; b = -28; c = -49;
Δ = b2-4ac
Δ = -282-4·12·(-49)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-56}{2*12}=\frac{-28}{24}
=-1+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+56}{2*12}=\frac{84}{24}
=3+1/2
$