x(x+1)=(x-1)(3x-5)

Solution for x(x+1)=(x-1)(3x-5) equation:

x(x+1)=(x-1)(3x-5)

We move all terms to the left:

x(x+1)-((x-1)(3x-5))=0

We multiply parentheses

x^2+x-((x-1)(3x-5))=0

We multiply parentheses ..

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


We calculate terms in parentheses: -((+3x^2-5x-3x+5)), so:

(+3x^2-5x-3x+5)

We get rid of parentheses

3x^2-5x-3x+5

We add all the numbers together, and all the variables

3x^2-8x+5

Back to the equation:

-(3x^2-8x+5)


We add all the numbers together, and all the variables

x^2+x-(3x^2-8x+5)=0

We get rid of parentheses

x^2-3x^2+x+8x-5=0

We add all the numbers together, and all the variables

-2x^2+9x-5=0

a = -2; b = 9; c = -5;
Δ = b2-4ac
Δ = 92-4·(-2)·(-5)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{41}}{2*-2}=\frac{-9-\sqrt{41}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{41}}{2*-2}=\frac{-9+\sqrt{41}}{-4}
$