3(a-6)=5-a(7+3a)

Solution for 3(a-6)=5-a(7+3a) equation:

3(a-6)=5-a(7+3a)

We move all terms to the left:

3(a-6)-(5-a(7+3a))=0

We add all the numbers together, and all the variables

3(a-6)-(5-a(3a+7))=0

We multiply parentheses

3a-(5-a(3a+7))-18=0


We calculate terms in parentheses: -(5-a(3a+7)), so:

5-a(3a+7)

determiningTheFunctionDomain
-a(3a+7)+5

We multiply parentheses

-3a^2-7a+5

Back to the equation:

-(-3a^2-7a+5)


We get rid of parentheses

3a^2+7a+3a-5-18=0

We add all the numbers together, and all the variables

3a^2+10a-23=0

a = 3; b = 10; c = -23;
Δ = b2-4ac
Δ = 102-4·3·(-23)
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{94}}{2*3}=\frac{-10-2\sqrt{94}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{94}}{2*3}=\frac{-10+2\sqrt{94}}{6}
$