9*(2x+1)=5x(x-2)

Solution for 9*(2x+1)=5x(x-2) equation:

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

We move all terms to the left:

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

We multiply parentheses

18x-(5x(x-2))+9=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 get rid of parentheses

-5x^2+18x+10x+9=0

We add all the numbers together, and all the variables

-5x^2+28x+9=0

a = -5; b = 28; c = +9;
Δ = b2-4ac
Δ = 282-4·(-5)·9
Δ = 964
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{964}=\sqrt{4*241}=\sqrt{4}*\sqrt{241}=2\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{241}}{2*-5}=\frac{-28-2\sqrt{241}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{241}}{2*-5}=\frac{-28+2\sqrt{241}}{-10}
$