8(x-1)-2x=x(x+50)

Solution for 8(x-1)-2x=x(x+50) equation:

8(x-1)-2x=x(x+50)

We move all terms to the left:

8(x-1)-2x-(x(x+50))=0

We add all the numbers together, and all the variables

-2x+8(x-1)-(x(x+50))=0

We multiply parentheses

-2x+8x-(x(x+50))-8=0


We calculate terms in parentheses: -(x(x+50)), so:

x(x+50)

We multiply parentheses

x^2+50x

Back to the equation:

-(x^2+50x)


We add all the numbers together, and all the variables

6x-(x^2+50x)-8=0

We get rid of parentheses

-x^2+6x-50x-8=0

We add all the numbers together, and all the variables

-1x^2-44x-8=0

a = -1; b = -44; c = -8;
Δ = b2-4ac
Δ = -442-4·(-1)·(-8)
Δ = 1904
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:

$\sqrt{\Delta}=\sqrt{1904}=\sqrt{16*119}=\sqrt{16}*\sqrt{119}=4\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{119}}{2*-1}=\frac{44-4\sqrt{119}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{119}}{2*-1}=\frac{44+4\sqrt{119}}{-2}
$