(14a+1)(a+1)=0

Solution for (14a+1)(a+1)=0 equation:

(14a+1)(a+1)=0

We multiply parentheses ..

(+14a^2+14a+a+1)=0

We get rid of parentheses

14a^2+14a+a+1=0

We add all the numbers together, and all the variables

14a^2+15a+1=0

a = 14; b = 15; c = +1;
Δ = b2-4ac
Δ = 152-4·14·1
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-13}{2*14}=\frac{-28}{28}
=-1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+13}{2*14}=\frac{-2}{28}
=-1/14
$