9=3/5a-6a

Solution for 9=3/5a-6a equation:

9=3/5a-6a

We move all terms to the left:

9-(3/5a-6a)=0


Domain of the equation: 5a-6a)!=0

a∈R


We add all the numbers together, and all the variables

-(-6a+3/5a)+9=0

We get rid of parentheses

6a-3/5a+9=0

We multiply all the terms by the denominator


6a*5a+9*5a-3=0

Wy multiply elements

30a^2+45a-3=0

a = 30; b = 45; c = -3;
Δ = b2-4ac
Δ = 452-4·30·(-3)
Δ = 2385
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:

$\sqrt{\Delta}=\sqrt{2385}=\sqrt{9*265}=\sqrt{9}*\sqrt{265}=3\sqrt{265}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{265}}{2*30}=\frac{-45-3\sqrt{265}}{60}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{265}}{2*30}=\frac{-45+3\sqrt{265}}{60}
$