(x-1)(4x/2x-1)=3.75

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Solution for (x-1)(4x/2x-1)=3.75 equation:



(x-1)(4x/2x-1)=3.75
We move all terms to the left:
(x-1)(4x/2x-1)-(3.75)=0
Domain of the equation: 2x-1)!=0
x∈R
We add all the numbers together, and all the variables
(x-1)(4x/2x-1)-3.75=0
We multiply parentheses ..
(+4x^2-1x-4x+1)-3.75=0
We get rid of parentheses
4x^2-1x-4x+1-3.75=0
We add all the numbers together, and all the variables
4x^2-5x-2.75=0
a = 4; b = -5; c = -2.75;
Δ = b2-4ac
Δ = -52-4·4·(-2.75)
Δ = 69
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{69}}{2*4}=\frac{5-\sqrt{69}}{8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{69}}{2*4}=\frac{5+\sqrt{69}}{8} $

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