2a(a+3)+4(1-a)=8

Solution for 2a(a+3)+4(1-a)=8 equation:

2a(a+3)+4(1-a)=8

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

2a^2+6a-4a+4-8=0

We add all the numbers together, and all the variables

2a^2+2a-4=0

a = 2; b = 2; c = -4;
Δ = b2-4ac
Δ = 22-4·2·(-4)
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{-(2)-6}{2*2}=\frac{-8}{4}
=-2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*2}=\frac{4}{4}
=1
$