3+x=7/8x

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

3+x=7/8x

We move all terms to the left:

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


Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x-7/8x+3=0

We multiply all the terms by the denominator


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

Wy multiply elements

8x^2+24x-7=0

a = 8; b = 24; c = -7;
Δ = b2-4ac
Δ = 242-4·8·(-7)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-20\sqrt{2}}{2*8}=\frac{-24-20\sqrt{2}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+20\sqrt{2}}{2*8}=\frac{-24+20\sqrt{2}}{16}
$