3(a-1)=4a(a-1.5)

Solution for 3(a-1)=4a(a-1.5) equation:

3(a-1)=4a(a-1.5)

We move all terms to the left:

3(a-1)-(4a(a-1.5))=0

We multiply parentheses

3a-(4a(a-1.5))-3=0


We calculate terms in parentheses: -(4a(a-1.5)), so:

4a(a-1.5)

We multiply parentheses

4a^2-6a

Back to the equation:

-(4a^2-6a)


We get rid of parentheses

-4a^2+3a+6a-3=0

We add all the numbers together, and all the variables

-4a^2+9a-3=0

a = -4; b = 9; c = -3;
Δ = b2-4ac
Δ = 92-4·(-4)·(-3)
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{-(9)-\sqrt{33}}{2*-4}=\frac{-9-\sqrt{33}}{-8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{33}}{2*-4}=\frac{-9+\sqrt{33}}{-8}
$