x-1=-1/8x+21

Solution for x-1=-1/8x+21 equation:

x-1=-1/8x+21

We move all terms to the left:

x-1-(-1/8x+21)=0


Domain of the equation: 8x+21)!=0

x∈R


We get rid of parentheses

x+1/8x-21-1=0

We multiply all the terms by the denominator


x*8x-21*8x-1*8x+1=0

Wy multiply elements

8x^2-168x-8x+1=0

We add all the numbers together, and all the variables

8x^2-176x+1=0

a = 8; b = -176; c = +1;
Δ = b2-4ac
Δ = -1762-4·8·1
Δ = 30944
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:

$\sqrt{\Delta}=\sqrt{30944}=\sqrt{16*1934}=\sqrt{16}*\sqrt{1934}=4\sqrt{1934}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-176)-4\sqrt{1934}}{2*8}=\frac{176-4\sqrt{1934}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-176)+4\sqrt{1934}}{2*8}=\frac{176+4\sqrt{1934}}{16}
$