8-3/7x=38+x

Solution for 8-3/7x=38+x equation:

8-3/7x=38+x

We move all terms to the left:

8-3/7x-(38+x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-3/7x-(x+38)+8=0

We get rid of parentheses

-3/7x-x-38+8=0

We multiply all the terms by the denominator


-x*7x-38*7x+8*7x-3=0

Wy multiply elements

-7x^2-266x+56x-3=0

We add all the numbers together, and all the variables

-7x^2-210x-3=0

a = -7; b = -210; c = -3;
Δ = b2-4ac
Δ = -2102-4·(-7)·(-3)
Δ = 44016
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:

$\sqrt{\Delta}=\sqrt{44016}=\sqrt{16*2751}=\sqrt{16}*\sqrt{2751}=4\sqrt{2751}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-4\sqrt{2751}}{2*-7}=\frac{210-4\sqrt{2751}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+4\sqrt{2751}}{2*-7}=\frac{210+4\sqrt{2751}}{-14}
$