10/8x+8x=21

Solution for 10/8x+8x=21 equation:

10/8x+8x=21

We move all terms to the left:

10/8x+8x-(21)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

8x+10/8x-21=0

We multiply all the terms by the denominator


8x*8x-21*8x+10=0

Wy multiply elements

64x^2-168x+10=0

a = 64; b = -168; c = +10;
Δ = b2-4ac
Δ = -1682-4·64·10
Δ = 25664
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:

$\sqrt{\Delta}=\sqrt{25664}=\sqrt{64*401}=\sqrt{64}*\sqrt{401}=8\sqrt{401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-8\sqrt{401}}{2*64}=\frac{168-8\sqrt{401}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+8\sqrt{401}}{2*64}=\frac{168+8\sqrt{401}}{128}
$