5/4x+3x=10

Solution for 5/4x+3x=10 equation:

5/4x+3x=10

We move all terms to the left:

5/4x+3x-(10)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3x+5/4x-10=0

We multiply all the terms by the denominator


3x*4x-10*4x+5=0

Wy multiply elements

12x^2-40x+5=0

a = 12; b = -40; c = +5;
Δ = b2-4ac
Δ = -402-4·12·5
Δ = 1360
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:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{85}}{2*12}=\frac{40-4\sqrt{85}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{85}}{2*12}=\frac{40+4\sqrt{85}}{24}
$