(2x-1)(4x+5)=(2x-1)(6x-x)

Solution for (2x-1)(4x+5)=(2x-1)(6x-x) equation:

(2x-1)(4x+5)=(2x-1)(6x-x)

We move all terms to the left:

(2x-1)(4x+5)-((2x-1)(6x-x))=0

We add all the numbers together, and all the variables

(2x-1)(4x+5)-((2x-1)(+5x))=0

We multiply parentheses ..

(+8x^2+10x-4x-5)-((2x-1)(+5x))=0


We calculate terms in parentheses: -((2x-1)(+5x)), so:

(2x-1)(+5x)

We multiply parentheses ..

(+10x^2-5x)

We get rid of parentheses

10x^2-5x

Back to the equation:

-(10x^2-5x)


We get rid of parentheses

8x^2-10x^2+10x-4x+5x-5=0

We add all the numbers together, and all the variables

-2x^2+11x-5=0

a = -2; b = 11; c = -5;
Δ = b2-4ac
Δ = 112-4·(-2)·(-5)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-9}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+9}{2*-2}=\frac{-2}{-4}
=1/2
$