500/35x=55x

Solution for 500/35x=55x equation:

500/35x=55x

We move all terms to the left:

500/35x-(55x)=0


Domain of the equation: 35x!=0

x!=0/35

x!=0

x∈R


We add all the numbers together, and all the variables

-55x+500/35x=0

We multiply all the terms by the denominator


-55x*35x+500=0

Wy multiply elements

-1925x^2+500=0

a = -1925; b = 0; c = +500;
Δ = b2-4ac
Δ = 02-4·(-1925)·500
Δ = 3850000
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:

$\sqrt{\Delta}=\sqrt{3850000}=\sqrt{10000*385}=\sqrt{10000}*\sqrt{385}=100\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{385}}{2*-1925}=\frac{0-100\sqrt{385}}{-3850}
=-\frac{100\sqrt{385}}{-3850}
=-\frac{2\sqrt{385}}{-77}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{385}}{2*-1925}=\frac{0+100\sqrt{385}}{-3850}
=\frac{100\sqrt{385}}{-3850}
=\frac{2\sqrt{385}}{-77}
$