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

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

(X+5)(2X-9)=(2X-9)(2X-9)

We move all terms to the left:

(X+5)(2X-9)-((2X-9)(2X-9))=0

We multiply parentheses ..

(+2X^2-9X+10X-45)-((2X-9)(2X-9))=0


We calculate terms in parentheses: -((2X-9)(2X-9)), so:

(2X-9)(2X-9)

We multiply parentheses ..

(+4X^2-18X-18X+81)

We get rid of parentheses

4X^2-18X-18X+81

We add all the numbers together, and all the variables

4X^2-36X+81

Back to the equation:

-(4X^2-36X+81)


We get rid of parentheses

2X^2-4X^2-9X+10X+36X-45-81=0

We add all the numbers together, and all the variables

-2X^2+37X-126=0

a = -2; b = 37; c = -126;
Δ = b2-4ac
Δ = 372-4·(-2)·(-126)
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{-(37)-19}{2*-2}=\frac{-56}{-4}
=+14
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+19}{2*-2}=\frac{-18}{-4}
=4+1/2
$