31/7x+28=4x+34

Solution for 31/7x+28=4x+34 equation:

31/7x+28=4x+34

We move all terms to the left:

31/7x+28-(4x+34)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

31/7x-4x-34+28=0

We multiply all the terms by the denominator


-4x*7x-34*7x+28*7x+31=0

Wy multiply elements

-28x^2-238x+196x+31=0

We add all the numbers together, and all the variables

-28x^2-42x+31=0

a = -28; b = -42; c = +31;
Δ = b2-4ac
Δ = -422-4·(-28)·31
Δ = 5236
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5236}=\sqrt{4*1309}=\sqrt{4}*\sqrt{1309}=2\sqrt{1309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{1309}}{2*-28}=\frac{42-2\sqrt{1309}}{-56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{1309}}{2*-28}=\frac{42+2\sqrt{1309}}{-56}
$