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

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}
$