(2x+5)(x+6)=(4x-9)(2x+5)

Solution for (2x+5)(x+6)=(4x-9)(2x+5) equation:

(2x+5)(x+6)=(4x-9)(2x+5)

We move all terms to the left:

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

We multiply parentheses ..

(+2x^2+12x+5x+30)-((4x-9)(2x+5))=0


We calculate terms in parentheses: -((4x-9)(2x+5)), so:

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

We multiply parentheses ..

(+8x^2+20x-18x-45)

We get rid of parentheses

8x^2+20x-18x-45

We add all the numbers together, and all the variables

8x^2+2x-45

Back to the equation:

-(8x^2+2x-45)


We get rid of parentheses

2x^2-8x^2+12x+5x-2x+30+45=0

We add all the numbers together, and all the variables

-6x^2+15x+75=0

a = -6; b = 15; c = +75;
Δ = b2-4ac
Δ = 152-4·(-6)·75
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-45}{2*-6}=\frac{-60}{-12}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+45}{2*-6}=\frac{30}{-12}
=-2+1/2
$