3a+5a(a-2)=6(a+4)

Solution for 3a+5a(a-2)=6(a+4) equation:

3a+5a(a-2)=6(a+4)

We move all terms to the left:

3a+5a(a-2)-(6(a+4))=0

We multiply parentheses

5a^2+3a-10a-(6(a+4))=0


We calculate terms in parentheses: -(6(a+4)), so:

6(a+4)

We multiply parentheses

6a+24

Back to the equation:

-(6a+24)


We add all the numbers together, and all the variables

5a^2-7a-(6a+24)=0

We get rid of parentheses

5a^2-7a-6a-24=0

We add all the numbers together, and all the variables

5a^2-13a-24=0

a = 5; b = -13; c = -24;
Δ = b2-4ac
Δ = -132-4·5·(-24)
Δ = 649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{649}}{2*5}=\frac{13-\sqrt{649}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{649}}{2*5}=\frac{13+\sqrt{649}}{10}
$