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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((x-1)(5x+4)), so:

(x-1)(5x+4)

We multiply parentheses ..

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

We get rid of parentheses

5x^2+4x-5x-4

We add all the numbers together, and all the variables

5x^2-1x-4

Back to the equation:

-(5x^2-1x-4)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2+4x-1=0

a = -3; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·(-3)·(-1)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2}{2*-3}=\frac{-6}{-6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2}{2*-3}=\frac{-2}{-6}
=1/3
$