-4a(a+2)=5(3a-1)+16

Solution for -4a(a+2)=5(3a-1)+16 equation:

-4a(a+2)=5(3a-1)+16

We move all terms to the left:

-4a(a+2)-(5(3a-1)+16)=0

We multiply parentheses

-4a^2-8a-(5(3a-1)+16)=0


We calculate terms in parentheses: -(5(3a-1)+16), so:

5(3a-1)+16

We multiply parentheses

15a-5+16

We add all the numbers together, and all the variables

15a+11

Back to the equation:

-(15a+11)


We get rid of parentheses

-4a^2-8a-15a-11=0

We add all the numbers together, and all the variables

-4a^2-23a-11=0

a = -4; b = -23; c = -11;
Δ = b2-4ac
Δ = -232-4·(-4)·(-11)
Δ = 353
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{-(-23)-\sqrt{353}}{2*-4}=\frac{23-\sqrt{353}}{-8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{353}}{2*-4}=\frac{23+\sqrt{353}}{-8}
$