15-5x=(4x+1)(x-1)

Solution for 15-5x=(4x+1)(x-1) equation:

15-5x=(4x+1)(x-1)

We move all terms to the left:

15-5x-((4x+1)(x-1))=0

We multiply parentheses ..

-((+4x^2-4x+x-1))-5x+15=0


We calculate terms in parentheses: -((+4x^2-4x+x-1)), so:

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

We get rid of parentheses

4x^2-4x+x-1

We add all the numbers together, and all the variables

4x^2-3x-1

Back to the equation:

-(4x^2-3x-1)


We add all the numbers together, and all the variables

-5x-(4x^2-3x-1)+15=0

We get rid of parentheses

-4x^2-5x+3x+1+15=0

We add all the numbers together, and all the variables

-4x^2-2x+16=0

a = -4; b = -2; c = +16;
Δ = b2-4ac
Δ = -22-4·(-4)·16
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{65}}{2*-4}=\frac{2-2\sqrt{65}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{65}}{2*-4}=\frac{2+2\sqrt{65}}{-8}
$