5x-10.2/4x=1

Solution for 5x-10.2/4x=1 equation:

5x-10.2/4x=1

We move all terms to the left:

5x-10.2/4x-(1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


5x*4x-1*4x-10.2=0

Wy multiply elements

20x^2-4x-10.2=0

a = 20; b = -4; c = -10.2;
Δ = b2-4ac
Δ = -42-4·20·(-10.2)
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{13}}{2*20}=\frac{4-8\sqrt{13}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{13}}{2*20}=\frac{4+8\sqrt{13}}{40}
$