5/8x+27=x

Solution for 5/8x+27=x equation:

5/8x+27=x

We move all terms to the left:

5/8x+27-(x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+5/8x+27=0

We multiply all the terms by the denominator


-1x*8x+27*8x+5=0

Wy multiply elements

-8x^2+216x+5=0

a = -8; b = 216; c = +5;
Δ = b2-4ac
Δ = 2162-4·(-8)·5
Δ = 46816
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:

$\sqrt{\Delta}=\sqrt{46816}=\sqrt{16*2926}=\sqrt{16}*\sqrt{2926}=4\sqrt{2926}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-4\sqrt{2926}}{2*-8}=\frac{-216-4\sqrt{2926}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+4\sqrt{2926}}{2*-8}=\frac{-216+4\sqrt{2926}}{-16}
$