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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-10x^2+18x-(-5(-3x+2))=0


We calculate terms in parentheses: -(-5(-3x+2)), so:

-5(-3x+2)

We multiply parentheses

15x-10

Back to the equation:

-(15x-10)


We get rid of parentheses

-10x^2+18x-15x+10=0

We add all the numbers together, and all the variables

-10x^2+3x+10=0

a = -10; b = 3; c = +10;
Δ = b2-4ac
Δ = 32-4·(-10)·10
Δ = 409
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{-(3)-\sqrt{409}}{2*-10}=\frac{-3-\sqrt{409}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{409}}{2*-10}=\frac{-3+\sqrt{409}}{-20}
$