3/7x+4=2x-1

Solution for 3/7x+4=2x-1 equation:

3/7x+4=2x-1

We move all terms to the left:

3/7x+4-(2x-1)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

3/7x-2x+1+4=0

We multiply all the terms by the denominator


-2x*7x+1*7x+4*7x+3=0

Wy multiply elements

-14x^2+7x+28x+3=0

We add all the numbers together, and all the variables

-14x^2+35x+3=0

a = -14; b = 35; c = +3;
Δ = b2-4ac
Δ = 352-4·(-14)·3
Δ = 1393
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-\sqrt{1393}}{2*-14}=\frac{-35-\sqrt{1393}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{1393}}{2*-14}=\frac{-35+\sqrt{1393}}{-28}
$