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

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

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

We move all terms to the left:

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

We get rid of parentheses

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


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

5x(x+2)

We multiply parentheses

5x^2+10x

Back to the equation:

-(5x^2+10x)


We add all the numbers together, and all the variables

7x-(5x^2+10x)+3=0

We get rid of parentheses

-5x^2+7x-10x+3=0

We add all the numbers together, and all the variables

-5x^2-3x+3=0

a = -5; b = -3; c = +3;
Δ = b2-4ac
Δ = -32-4·(-5)·3
Δ = 69
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{69}}{2*-5}=\frac{3-\sqrt{69}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{69}}{2*-5}=\frac{3+\sqrt{69}}{-10}
$