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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

2x-(-3x(-1x+5))-9=0


We calculate terms in parentheses: -(-3x(-1x+5)), so:

-3x(-1x+5)

We multiply parentheses

3x^2-15x

Back to the equation:

-(3x^2-15x)


We get rid of parentheses

-3x^2+2x+15x-9=0

We add all the numbers together, and all the variables

-3x^2+17x-9=0

a = -3; b = 17; c = -9;
Δ = b2-4ac
Δ = 172-4·(-3)·(-9)
Δ = 181
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{-(17)-\sqrt{181}}{2*-3}=\frac{-17-\sqrt{181}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{181}}{2*-3}=\frac{-17+\sqrt{181}}{-6}
$