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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+9x^2-3x+18x-6)-(5x(4x-2))=0


We calculate terms in parentheses: -(5x(4x-2)), so:

5x(4x-2)

We multiply parentheses

20x^2-10x

Back to the equation:

-(20x^2-10x)


We get rid of parentheses

9x^2-20x^2-3x+18x+10x-6=0

We add all the numbers together, and all the variables

-11x^2+25x-6=0

a = -11; b = 25; c = -6;
Δ = b2-4ac
Δ = 252-4·(-11)·(-6)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-19}{2*-11}=\frac{-44}{-22}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+19}{2*-11}=\frac{-6}{-22}
=3/11
$