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

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

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

We multiply parentheses ..

(+12x^2+4x+42x+14)=0

We get rid of parentheses

12x^2+4x+42x+14=0

We add all the numbers together, and all the variables

12x^2+46x+14=0

a = 12; b = 46; c = +14;
Δ = b2-4ac
Δ = 462-4·12·14
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-38}{2*12}=\frac{-84}{24}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+38}{2*12}=\frac{-8}{24}
=-1/3
$