x+10/8x=540

Solution for x+10/8x=540 equation:

x+10/8x=540

We move all terms to the left:

x+10/8x-(540)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We multiply all the terms by the denominator


x*8x-540*8x+10=0

Wy multiply elements

8x^2-4320x+10=0

a = 8; b = -4320; c = +10;
Δ = b2-4ac
Δ = -43202-4·8·10
Δ = 18662080
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:

$\sqrt{\Delta}=\sqrt{18662080}=\sqrt{64*291595}=\sqrt{64}*\sqrt{291595}=8\sqrt{291595}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4320)-8\sqrt{291595}}{2*8}=\frac{4320-8\sqrt{291595}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4320)+8\sqrt{291595}}{2*8}=\frac{4320+8\sqrt{291595}}{16}
$