17+8x=5x(x-1)

Solution for 17+8x=5x(x-1) equation:

17+8x=5x(x-1)

We move all terms to the left:

17+8x-(5x(x-1))=0


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

5x(x-1)

We multiply parentheses

5x^2-5x

Back to the equation:

-(5x^2-5x)


We get rid of parentheses

-5x^2+8x+5x+17=0

We add all the numbers together, and all the variables

-5x^2+13x+17=0

a = -5; b = 13; c = +17;
Δ = b2-4ac
Δ = 132-4·(-5)·17
Δ = 509
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{-(13)-\sqrt{509}}{2*-5}=\frac{-13-\sqrt{509}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{509}}{2*-5}=\frac{-13+\sqrt{509}}{-10}
$