23/7x=3x+8

Solution for 23/7x=3x+8 equation:

23/7x=3x+8

We move all terms to the left:

23/7x-(3x+8)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

23/7x-3x-8=0

We multiply all the terms by the denominator


-3x*7x-8*7x+23=0

Wy multiply elements

-21x^2-56x+23=0

a = -21; b = -56; c = +23;
Δ = b2-4ac
Δ = -562-4·(-21)·23
Δ = 5068
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:

$\sqrt{\Delta}=\sqrt{5068}=\sqrt{4*1267}=\sqrt{4}*\sqrt{1267}=2\sqrt{1267}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-2\sqrt{1267}}{2*-21}=\frac{56-2\sqrt{1267}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+2\sqrt{1267}}{2*-21}=\frac{56+2\sqrt{1267}}{-42}
$