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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


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

(2x-1)(x-1)

We multiply parentheses ..

(+2x^2-2x-1x+1)

We get rid of parentheses

2x^2-2x-1x+1

We add all the numbers together, and all the variables

2x^2-3x+1

Back to the equation:

-(2x^2-3x+1)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+8x+3=0

a = -1; b = 8; c = +3;
Δ = b2-4ac
Δ = 82-4·(-1)·3
Δ = 76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{19}}{2*-1}=\frac{-8-2\sqrt{19}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{19}}{2*-1}=\frac{-8+2\sqrt{19}}{-2}
$