.(-6+7a)+(14-6a)=8

Solution for .(-6+7a)+(14-6a)=8 equation:

.(-6+7a)+(14-6a)=8

We move all terms to the left:

.(-6+7a)+(14-6a)-(8)=0

We add all the numbers together, and all the variables

.(7a-6)+(-6a+14)-8=0

We multiply parentheses

7a^2+(-6a+14)-8+=0

We get rid of parentheses

7a^2-6a+14-8+=0

We add all the numbers together, and all the variables

7a^2-6a=0

a = 7; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·7·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*7}=\frac{0}{14}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*7}=\frac{12}{14}
=6/7
$