1/8x+5=-16x+32

Solution for 1/8x+5=-16x+32 equation:

1/8x+5=-16x+32

We move all terms to the left:

1/8x+5-(-16x+32)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

1/8x+16x-32+5=0

We multiply all the terms by the denominator


16x*8x-32*8x+5*8x+1=0

Wy multiply elements

128x^2-256x+40x+1=0

We add all the numbers together, and all the variables

128x^2-216x+1=0

a = 128; b = -216; c = +1;
Δ = b2-4ac
Δ = -2162-4·128·1
Δ = 46144
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:

$\sqrt{\Delta}=\sqrt{46144}=\sqrt{64*721}=\sqrt{64}*\sqrt{721}=8\sqrt{721}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-8\sqrt{721}}{2*128}=\frac{216-8\sqrt{721}}{256}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+8\sqrt{721}}{2*128}=\frac{216+8\sqrt{721}}{256}
$