3a(a+1)=19-5a

Solution for 3a(a+1)=19-5a equation:

3a(a+1)=19-5a

We move all terms to the left:

3a(a+1)-(19-5a)=0

We add all the numbers together, and all the variables

3a(a+1)-(-5a+19)=0

We multiply parentheses

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

We get rid of parentheses

3a^2+3a+5a-19=0

We add all the numbers together, and all the variables

3a^2+8a-19=0

a = 3; b = 8; c = -19;
Δ = b2-4ac
Δ = 82-4·3·(-19)
Δ = 292
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{73}}{2*3}=\frac{-8-2\sqrt{73}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{73}}{2*3}=\frac{-8+2\sqrt{73}}{6}
$