5=2a(3a+1)

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

5=2a(3a+1)

We move all terms to the left:

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


We calculate terms in parentheses: -(2a(3a+1)), so:

2a(3a+1)

We multiply parentheses

6a^2+2a

Back to the equation:

-(6a^2+2a)


We get rid of parentheses

-6a^2-2a+5=0

a = -6; b = -2; c = +5;
Δ = b2-4ac
Δ = -22-4·(-6)·5
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{31}}{2*-6}=\frac{2-2\sqrt{31}}{-12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{31}}{2*-6}=\frac{2+2\sqrt{31}}{-12}
$