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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+2x^2-6x+5x-15)-((x-3)(x-4))=0


We calculate terms in parentheses: -((x-3)(x-4)), so:

(x-3)(x-4)

We multiply parentheses ..

(+x^2-4x-3x+12)

We get rid of parentheses

x^2-4x-3x+12

We add all the numbers together, and all the variables

x^2-7x+12

Back to the equation:

-(x^2-7x+12)


We get rid of parentheses

2x^2-x^2-6x+5x+7x-15-12=0

We add all the numbers together, and all the variables

x^2+6x-27=0

a = 1; b = 6; c = -27;
Δ = b2-4ac
Δ = 62-4·1·(-27)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12}{2*1}=\frac{6}{2}
=3
$