x/4x-2(3x-5)=8x-50

Solution for x/4x-2(3x-5)=8x-50 equation:

x/4x-2(3x-5)=8x-50

We move all terms to the left:

x/4x-2(3x-5)-(8x-50)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply parentheses

x/4x-6x-(8x-50)+10=0

We get rid of parentheses

x/4x-6x-8x+50+10=0

We multiply all the terms by the denominator


x-6x*4x-8x*4x+50*4x+10*4x=0

Wy multiply elements

-24x^2-32x^2+x+200x+40x=0

We add all the numbers together, and all the variables

-56x^2+241x=0

a = -56; b = 241; c = 0;
Δ = b2-4ac
Δ = 2412-4·(-56)·0
Δ = 58081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{58081}=241$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(241)-241}{2*-56}=\frac{-482}{-112}
=4+17/56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(241)+241}{2*-56}=\frac{0}{-112}
=0
$