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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


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

(-3a+2)a

We multiply parentheses

-3a^2+2a

Back to the equation:

-(-3a^2+2a)


We get rid of parentheses

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

We add all the numbers together, and all the variables

8a^2-7a=0

a = 8; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·8·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*8}=\frac{0}{16}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*8}=\frac{14}{16}
=7/8
$