5/4x=2x-1

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Solution for 5/4x=2x-1 equation:



5/4x=2x-1
We move all terms to the left:
5/4x-(2x-1)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
We get rid of parentheses
5/4x-2x+1=0
We multiply all the terms by the denominator
-2x*4x+1*4x+5=0
Wy multiply elements
-8x^2+4x+5=0
a = -8; b = 4; c = +5;
Δ = b2-4ac
Δ = 42-4·(-8)·5
Δ = 176
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:
$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{11}}{2*-8}=\frac{-4-4\sqrt{11}}{-16} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{11}}{2*-8}=\frac{-4+4\sqrt{11}}{-16} $

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