3(1-9a)22a=2(2a-9)-15

Solution for 3(1-9a)22a=2(2a-9)-15 equation:

3(1-9a)22a=2(2a-9)-15

We move all terms to the left:

3(1-9a)22a-(2(2a-9)-15)=0

We add all the numbers together, and all the variables

3(-9a+1)22a-(2(2a-9)-15)=0

We multiply parentheses

-594a^2+66a-(2(2a-9)-15)=0


We calculate terms in parentheses: -(2(2a-9)-15), so:

2(2a-9)-15

We multiply parentheses

4a-18-15

We add all the numbers together, and all the variables

4a-33

Back to the equation:

-(4a-33)


We get rid of parentheses

-594a^2+66a-4a+33=0

We add all the numbers together, and all the variables

-594a^2+62a+33=0

a = -594; b = 62; c = +33;
Δ = b2-4ac
Δ = 622-4·(-594)·33
Δ = 82252
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:

$\sqrt{\Delta}=\sqrt{82252}=\sqrt{4*20563}=\sqrt{4}*\sqrt{20563}=2\sqrt{20563}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-2\sqrt{20563}}{2*-594}=\frac{-62-2\sqrt{20563}}{-1188}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+2\sqrt{20563}}{2*-594}=\frac{-62+2\sqrt{20563}}{-1188}
$