3a-25=11-3a(a+4)

Solution for 3a-25=11-3a(a+4) equation:

3a-25=11-3a(a+4)

We move all terms to the left:

3a-25-(11-3a(a+4))=0


We calculate terms in parentheses: -(11-3a(a+4)), so:

11-3a(a+4)

determiningTheFunctionDomain
-3a(a+4)+11

We multiply parentheses

-3a^2-12a+11

Back to the equation:

-(-3a^2-12a+11)


We get rid of parentheses

3a^2+12a+3a-11-25=0

We add all the numbers together, and all the variables

3a^2+15a-36=0

a = 3; b = 15; c = -36;
Δ = b2-4ac
Δ = 152-4·3·(-36)
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{73}}{2*3}=\frac{-15-3\sqrt{73}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{73}}{2*3}=\frac{-15+3\sqrt{73}}{6}
$