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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


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

-5a(3a+7)

We multiply parentheses

-15a^2-35a

Back to the equation:

-(-15a^2-35a)


We get rid of parentheses

15a^2+35a+3a-18=0

We add all the numbers together, and all the variables

15a^2+38a-18=0

a = 15; b = 38; c = -18;
Δ = b2-4ac
Δ = 382-4·15·(-18)
Δ = 2524
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:

$\sqrt{\Delta}=\sqrt{2524}=\sqrt{4*631}=\sqrt{4}*\sqrt{631}=2\sqrt{631}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{631}}{2*15}=\frac{-38-2\sqrt{631}}{30}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{631}}{2*15}=\frac{-38+2\sqrt{631}}{30}
$