5/2x+23/4x=5

Solution for 5/2x+23/4x=5 equation:

5/2x+23/4x=5

We move all terms to the left:

5/2x+23/4x-(5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


20x/8x^2+46x/8x^2-5=0

We multiply all the terms by the denominator


20x+46x-5*8x^2=0

We add all the numbers together, and all the variables

66x-5*8x^2=0

Wy multiply elements

-40x^2+66x=0

a = -40; b = 66; c = 0;
Δ = b2-4ac
Δ = 662-4·(-40)·0
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-66}{2*-40}=\frac{-132}{-80}
=1+13/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+66}{2*-40}=\frac{0}{-80}
=0
$