x/5x-14=8x+4

Solution for x/5x-14=8x+4 equation:

x/5x-14=8x+4

We move all terms to the left:

x/5x-14-(8x+4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

x/5x-8x-4-14=0

We multiply all the terms by the denominator


x-8x*5x-4*5x-14*5x=0

Wy multiply elements

-40x^2+x-20x-70x=0

We add all the numbers together, and all the variables

-40x^2-89x=0

a = -40; b = -89; c = 0;
Δ = b2-4ac
Δ = -892-4·(-40)·0
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-89)-89}{2*-40}=\frac{0}{-80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+89}{2*-40}=\frac{178}{-80}
=-2+9/40
$