2(a+3)(2a-1)=19

Solution for 2(a+3)(2a-1)=19 equation:

2(a+3)(2a-1)=19

We move all terms to the left:

2(a+3)(2a-1)-(19)=0

We multiply parentheses ..

2(+2a^2-1a+6a-3)-19=0

We multiply parentheses

4a^2-2a+12a-6-19=0

We add all the numbers together, and all the variables

4a^2+10a-25=0

a = 4; b = 10; c = -25;
Δ = b2-4ac
Δ = 102-4·4·(-25)
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{5}}{2*4}=\frac{-10-10\sqrt{5}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{5}}{2*4}=\frac{-10+10\sqrt{5}}{8}
$