(4a-3)=a(2a-1)

Solution for (4a-3)=a(2a-1) equation:

(4a-3)=a(2a-1)

We move all terms to the left:

(4a-3)-(a(2a-1))=0

We get rid of parentheses

4a-(a(2a-1))-3=0


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

a(2a-1)

We multiply parentheses

2a^2-1a

Back to the equation:

-(2a^2-1a)


We get rid of parentheses

-2a^2+4a+1a-3=0

We add all the numbers together, and all the variables

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

a = -2; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·(-2)·(-3)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-1}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+1}{2*-2}=\frac{-4}{-4}
=1
$