5/7x+4=14-1/2x

Solution for 5/7x+4=14-1/2x equation:

5/7x+4=14-1/2x

We move all terms to the left:

5/7x+4-(14-1/2x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/7x-(-1/2x+14)+4=0

We get rid of parentheses

5/7x+1/2x-14+4=0

We calculate fractions


10x/14x^2+7x/14x^2-14+4=0

We add all the numbers together, and all the variables

10x/14x^2+7x/14x^2-10=0

We multiply all the terms by the denominator


10x+7x-10*14x^2=0

We add all the numbers together, and all the variables

17x-10*14x^2=0

Wy multiply elements

-140x^2+17x=0

a = -140; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-140)·0
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{-(17)-17}{2*-140}=\frac{-34}{-280}
=17/140
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-140}=\frac{0}{-280}
=0
$