5/4x-5(x-2)=1

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

5/4x-5(x-2)=1

We move all terms to the left:

5/4x-5(x-2)-(1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply parentheses

5/4x-5x+10-1=0

We multiply all the terms by the denominator


-5x*4x+10*4x-1*4x+5=0

Wy multiply elements

-20x^2+40x-4x+5=0

We add all the numbers together, and all the variables

-20x^2+36x+5=0

a = -20; b = 36; c = +5;
Δ = b2-4ac
Δ = 362-4·(-20)·5
Δ = 1696
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:

$\sqrt{\Delta}=\sqrt{1696}=\sqrt{16*106}=\sqrt{16}*\sqrt{106}=4\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{106}}{2*-20}=\frac{-36-4\sqrt{106}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{106}}{2*-20}=\frac{-36+4\sqrt{106}}{-40}
$