-3a-1=2a(a+7)

Solution for -3a-1=2a(a+7) equation:

-3a-1=2a(a+7)

We move all terms to the left:

-3a-1-(2a(a+7))=0


We calculate terms in parentheses: -(2a(a+7)), so:

2a(a+7)

We multiply parentheses

2a^2+14a

Back to the equation:

-(2a^2+14a)


We get rid of parentheses

-2a^2-3a-14a-1=0

We add all the numbers together, and all the variables

-2a^2-17a-1=0

a = -2; b = -17; c = -1;
Δ = b2-4ac
Δ = -172-4·(-2)·(-1)
Δ = 281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{281}}{2*-2}=\frac{17-\sqrt{281}}{-4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{281}}{2*-2}=\frac{17+\sqrt{281}}{-4}
$