2(3a+4)-9a=3a(a+5)

Solution for 2(3a+4)-9a=3a(a+5) equation:

2(3a+4)-9a=3a(a+5)

We move all terms to the left:

2(3a+4)-9a-(3a(a+5))=0

We add all the numbers together, and all the variables

-9a+2(3a+4)-(3a(a+5))=0

We multiply parentheses

-9a+6a-(3a(a+5))+8=0


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

3a(a+5)

We multiply parentheses

3a^2+15a

Back to the equation:

-(3a^2+15a)


We add all the numbers together, and all the variables

-3a-(3a^2+15a)+8=0

We get rid of parentheses

-3a^2-3a-15a+8=0

We add all the numbers together, and all the variables

-3a^2-18a+8=0

a = -3; b = -18; c = +8;
Δ = b2-4ac
Δ = -182-4·(-3)·8
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{105}}{2*-3}=\frac{18-2\sqrt{105}}{-6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{105}}{2*-3}=\frac{18+2\sqrt{105}}{-6}
$