1/215x-45=5x

Solution for 1/215x-45=5x equation:

1/215x-45=5x

We move all terms to the left:

1/215x-45-(5x)=0


Domain of the equation: 215x!=0

x!=0/215

x!=0

x∈R


We add all the numbers together, and all the variables

-5x+1/215x-45=0

We multiply all the terms by the denominator


-5x*215x-45*215x+1=0

Wy multiply elements

-1075x^2-9675x+1=0

a = -1075; b = -9675; c = +1;
Δ = b2-4ac
Δ = -96752-4·(-1075)·1
Δ = 93609925
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:

$\sqrt{\Delta}=\sqrt{93609925}=\sqrt{70225*1333}=\sqrt{70225}*\sqrt{1333}=265\sqrt{1333}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9675)-265\sqrt{1333}}{2*-1075}=\frac{9675-265\sqrt{1333}}{-2150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9675)+265\sqrt{1333}}{2*-1075}=\frac{9675+265\sqrt{1333}}{-2150}
$