156/8x+10x=1360

Solution for 156/8x+10x=1360 equation:

156/8x+10x=1360

We move all terms to the left:

156/8x+10x-(1360)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

10x+156/8x-1360=0

We multiply all the terms by the denominator


10x*8x-1360*8x+156=0

Wy multiply elements

80x^2-10880x+156=0

a = 80; b = -10880; c = +156;
Δ = b2-4ac
Δ = -108802-4·80·156
Δ = 118324480
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:

$\sqrt{\Delta}=\sqrt{118324480}=\sqrt{256*462205}=\sqrt{256}*\sqrt{462205}=16\sqrt{462205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10880)-16\sqrt{462205}}{2*80}=\frac{10880-16\sqrt{462205}}{160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10880)+16\sqrt{462205}}{2*80}=\frac{10880+16\sqrt{462205}}{160}
$