a^2-6a=5/3

Solution for a^2-6a=5/3 equation:

a^2-6a=5/3

We move all terms to the left:

a^2-6a-(5/3)=0

We add all the numbers together, and all the variables

a^2-6a-(+5/3)=0

We get rid of parentheses

a^2-6a-5/3=0

We multiply all the terms by the denominator


a^2*3-6a*3-5=0

Wy multiply elements

3a^2-18a-5=0

a = 3; b = -18; c = -5;
Δ = b2-4ac
Δ = -182-4·3·(-5)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-8\sqrt{6}}{2*3}=\frac{18-8\sqrt{6}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+8\sqrt{6}}{2*3}=\frac{18+8\sqrt{6}}{6}
$