6-4a(a+1)=7+a

Solution for 6-4a(a+1)=7+a equation:

6-4a(a+1)=7+a

We move all terms to the left:

6-4a(a+1)-(7+a)=0

We add all the numbers together, and all the variables

-4a(a+1)-(a+7)+6=0

We multiply parentheses

-4a^2-4a-(a+7)+6=0

We get rid of parentheses

-4a^2-4a-a-7+6=0

We add all the numbers together, and all the variables

-4a^2-5a-1=0

a = -4; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·(-4)·(-1)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*-4}=\frac{2}{-8}
=-1/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*-4}=\frac{8}{-8}
=-1
$