5x-4*5/4x+5*0.25=121.49253731343

Solution for 5x-4*5/4x+5*0.25=121.49253731343 equation:

5x-4*5/4x+5*0.25=121.49253731343

We move all terms to the left:

5x-4*5/4x+5*0.25-(121.49253731343)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

5x-4*5/4x-120.24253731343=0

We multiply all the terms by the denominator


5x*4x-(120.24253731343)*4x-4*5=0

We add all the numbers together, and all the variables

5x*4x-(120.24253731343)*4x-20=0

We multiply parentheses

5x*4x-480.97014925372x-20=0

Wy multiply elements

20x^2-480.97014925372x-20=0

a = 20; b = -480.97014925372; c = -20;
Δ = b2-4ac
Δ = -480.970149253722-4·20·(-20)
Δ = 232932.28447315
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{-(-480.97014925372)-\sqrt{232932.28447315}}{2*20}=\frac{480.97014925372-\sqrt{232932.28447315}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480.97014925372)+\sqrt{232932.28447315}}{2*20}=\frac{480.97014925372+\sqrt{232932.28447315}}{40}
$