1/4x+5/2x=55/24

Solution for 1/4x+5/2x=55/24 equation:

1/4x+5/2x=55/24

We move all terms to the left:

1/4x+5/2x-(55/24)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x+5/2x-(+55/24)=0

We get rid of parentheses

1/4x+5/2x-55/24=0

We calculate fractions


(-880x^2)/384x^2+96x/384x^2+960x/384x^2=0

We multiply all the terms by the denominator


(-880x^2)+96x+960x=0

We add all the numbers together, and all the variables

(-880x^2)+1056x=0

We get rid of parentheses

-880x^2+1056x=0

a = -880; b = 1056; c = 0;
Δ = b2-4ac
Δ = 10562-4·(-880)·0
Δ = 1115136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1115136}=1056$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1056)-1056}{2*-880}=\frac{-2112}{-1760}
=1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1056)+1056}{2*-880}=\frac{0}{-1760}
=0
$