-3a(a+17)=3(a-5)

Solution for -3a(a+17)=3(a-5) equation:

-3a(a+17)=3(a-5)

We move all terms to the left:

-3a(a+17)-(3(a-5))=0

We multiply parentheses

-3a^2-51a-(3(a-5))=0


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

3(a-5)

We multiply parentheses

3a-15

Back to the equation:

-(3a-15)


We get rid of parentheses

-3a^2-51a-3a+15=0

We add all the numbers together, and all the variables

-3a^2-54a+15=0

a = -3; b = -54; c = +15;
Δ = b2-4ac
Δ = -542-4·(-3)·15
Δ = 3096
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:

$\sqrt{\Delta}=\sqrt{3096}=\sqrt{36*86}=\sqrt{36}*\sqrt{86}=6\sqrt{86}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{86}}{2*-3}=\frac{54-6\sqrt{86}}{-6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{86}}{2*-3}=\frac{54+6\sqrt{86}}{-6}
$