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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+x^2-4x+6x-24)-((2x+5)(x-4))=0


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

(2x+5)(x-4)

We multiply parentheses ..

(+2x^2-8x+5x-20)

We get rid of parentheses

2x^2-8x+5x-20

We add all the numbers together, and all the variables

2x^2-3x-20

Back to the equation:

-(2x^2-3x-20)


We get rid of parentheses

x^2-2x^2-4x+6x+3x-24+20=0

We add all the numbers together, and all the variables

-1x^2+5x-4=0

a = -1; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·(-1)·(-4)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3}{2*-1}=\frac{-2}{-2}
=1
$