-13+5a=3a(a-3)

Solution for -13+5a=3a(a-3) equation:

-13+5a=3a(a-3)

We move all terms to the left:

-13+5a-(3a(a-3))=0


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

3a(a-3)

We multiply parentheses

3a^2-9a

Back to the equation:

-(3a^2-9a)


We get rid of parentheses

-3a^2+5a+9a-13=0

We add all the numbers together, and all the variables

-3a^2+14a-13=0

a = -3; b = 14; c = -13;
Δ = b2-4ac
Δ = 142-4·(-3)·(-13)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{10}}{2*-3}=\frac{-14-2\sqrt{10}}{-6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{10}}{2*-3}=\frac{-14+2\sqrt{10}}{-6}
$