x=-1/8x+3

Solution for x=-1/8x+3 equation:

x=-1/8x+3

We move all terms to the left:

x-(-1/8x+3)=0


Domain of the equation: 8x+3)!=0

x∈R


We get rid of parentheses

x+1/8x-3=0

We multiply all the terms by the denominator


x*8x-3*8x+1=0

Wy multiply elements

8x^2-24x+1=0

a = 8; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·8·1
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{34}}{2*8}=\frac{24-4\sqrt{34}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{34}}{2*8}=\frac{24+4\sqrt{34}}{16}
$