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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-9a-15a-(4(-2a+3)a)+10=0


We calculate terms in parentheses: -(4(-2a+3)a), so:

4(-2a+3)a

We multiply parentheses

-8a^2+12a

Back to the equation:

-(-8a^2+12a)


We add all the numbers together, and all the variables

-(-8a^2+12a)-24a+10=0

We get rid of parentheses

8a^2-12a-24a+10=0

We add all the numbers together, and all the variables

8a^2-36a+10=0

a = 8; b = -36; c = +10;
Δ = b2-4ac
Δ = -362-4·8·10
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{61}}{2*8}=\frac{36-4\sqrt{61}}{16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{61}}{2*8}=\frac{36+4\sqrt{61}}{16}
$