-3x(5-2x)=6-(4x-9)

Solution for -3x(5-2x)=6-(4x-9) equation:

-3x(5-2x)=6-(4x-9)

We move all terms to the left:

-3x(5-2x)-(6-(4x-9))=0

We add all the numbers together, and all the variables

-3x(-2x+5)-(6-(4x-9))=0

We multiply parentheses

6x^2-15x-(6-(4x-9))=0


We calculate terms in parentheses: -(6-(4x-9)), so:

6-(4x-9)

determiningTheFunctionDomain
-(4x-9)+6

We get rid of parentheses

-4x+9+6

We add all the numbers together, and all the variables

-4x+15

Back to the equation:

-(-4x+15)


We get rid of parentheses

6x^2-15x+4x-15=0

We add all the numbers together, and all the variables

6x^2-11x-15=0

a = 6; b = -11; c = -15;
Δ = b2-4ac
Δ = -112-4·6·(-15)
Δ = 481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{481}}{2*6}=\frac{11-\sqrt{481}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{481}}{2*6}=\frac{11+\sqrt{481}}{12}
$