14-8x=5x(x-1)

Solution for 14-8x=5x(x-1) equation:

14-8x=5x(x-1)

We move all terms to the left:

14-8x-(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+14=0

We add all the numbers together, and all the variables

-5x^2-3x+14=0

a = -5; b = -3; c = +14;
Δ = b2-4ac
Δ = -32-4·(-5)·14
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-17}{2*-5}=\frac{-14}{-10}
=1+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+17}{2*-5}=\frac{20}{-10}
=-2
$