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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

2a^2-2a-3a-1=0

We add all the numbers together, and all the variables

2a^2-5a-1=0

a = 2; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·2·(-1)
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{33}}{2*2}=\frac{5-\sqrt{33}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{33}}{2*2}=\frac{5+\sqrt{33}}{4}
$