x/5x-14=8x+

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

x/5x-14=8x+

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x/5x-8x-14=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-40x^2-69x=0

a = -40; b = -69; c = 0;
Δ = b2-4ac
Δ = -692-4·(-40)·0
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-69}{2*-40}=\frac{0}{-80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+69}{2*-40}=\frac{138}{-80}
=-1+29/40
$