2(a-8)+8=5(a+2)3a-19

Solution for 2(a-8)+8=5(a+2)3a-19 equation:

2(a-8)+8=5(a+2)3a-19

We move all terms to the left:

2(a-8)+8-(5(a+2)3a-19)=0

We multiply parentheses

2a-(5(a+2)3a-19)-16+8=0


We calculate terms in parentheses: -(5(a+2)3a-19), so:

5(a+2)3a-19

We multiply parentheses

15a^2+30a-19

Back to the equation:

-(15a^2+30a-19)


We add all the numbers together, and all the variables

2a-(15a^2+30a-19)-8=0

We get rid of parentheses

-15a^2+2a-30a+19-8=0

We add all the numbers together, and all the variables

-15a^2-28a+11=0

a = -15; b = -28; c = +11;
Δ = b2-4ac
Δ = -282-4·(-15)·11
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-38}{2*-15}=\frac{-10}{-30}
=1/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+38}{2*-15}=\frac{66}{-30}
=-2+1/5
$